Nagayoshi Iwahori

Let ~t be a linear functional on E having E 1 for its kernel.With x any nonzero element of E, consider the quotient ]~t(x)I/a(x).First of all this quotient is continuous.Secondly, … Let ~t be a linear functional on E having E 1 for its kernel.With x any nonzero element of E, consider the quotient ]~t(x)I/a(x).First of all this quotient is continuous.Secondly, it is a homogeneous function of degree 0. Hence it defines a continuous function on the projective space P(E).As P(E) is compact, this function assumes its maximum.Thus, there is an element x~ E E such that I~(~)l< I~(~1)1 all xfiE. a(x) a(xl) 'It is clear that x 1 cannot be in E 1. Hence, E is the direct sum of Kx 1 and E 1.Let yEE; then y=xl2(y)/X(Xl)+Z, with zEE t.We have, on the one hand, /l~(y)l ), and, on the other hand, from the definition of Xl, that /> I~(y)l ~(~1) It follows that /I (y)I ~(y) = sup ~ ~(~1), ~(z)).From the inductive assumption, there is a basis x~ ..... xn of E 1 and positive real numbers r e ..... rn such that o~ a,x, = sup (% [az[ ..... rn lanl).If we set r 1 = a(xl), then the argument above shows that a(~ a,x,) = sup (r, ]a,I).If ae~(E), and {x,} is a basis such that a(ba, x,)=sup(r, la, l), then we shall say that a is canonical with respect to {x,}.We denote by E* the dual space of E. We shall now describe a useful mapping from ~(E) to ~(E*).Let a e~(E).If •eE*, we have already considered in the proof above, the quotient 12(x)l/a(x) for non-zero xeE.The continuity of this quotient and "the compactness of P(E) enable us to set a*(Z) = sup !Z(x) l a(x)There is no difficulty in verifying that a* is a norm on E*.

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On Real Irreducible Representations of Lie Algebras

1959-02-01

Nagayoshi Iwahori

Let us consider the following two problems: Problem A. Let g be a given Lie algebra over the real number field R. Then find all real, irreducible representations of g … Let us consider the following two problems: Problem A. Let g be a given Lie algebra over the real number field R. Then find all real, irreducible representations of g . Problem B. Let n be a given positive integer. Then find all irreducible subalgebras of the Lie algebra ôí(w, R) of all real matrices of degree n .

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Centralizers of involutions in finite Chevalley groups

1970-01-01

Nagayoshi Iwahori

Generalized Tits system (Bruhat decompostition) on 𝑝-adic semisimple groups

1966-01-01

Nagayoshi Iwahori

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A duality theorem for homogeneous manifolds of compact Lie groups

1966-06-01

Nagayoshi Iwahori , Mitsuo Sugiura

Some remarks on tensor invariants of $O(\mathfrak{n}),$ $U(n), Sp(n)$ .

1958-04-01

Nagayoshi Iwahori

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A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups

1965-04-01

Nagayoshi Iwahori , Takeshi Kondo

A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups

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A characterization of odd order extensions of the Ree groups ${}^2F_4(q)$

1975-03-25

Ken-ichi Shinoda , Nagayoshi Iwahori

On Cartan subalgebras of a Lie algebra

1950-01-01

Nagayoshi Iwahori , Ichirō Satake

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An Extension of Tannaka Duality Theorem for Homogeneous Spaces

1958-01-01

Nagayoshi Iwahori , Nobuko Iwahori

On primitive permutation groups of degree $2p=4q+2$ , p and q being prime numbers

1975-03-25

Izumi Miyamoto , Nagayoshi Iwahori

On a set of generating relations of the full transformation semigroups

1974-03-01

Nagayoshi Iwahori , Nobuko Iwahori

On self-dual, completely reducible finite subgroups of $GL (2, k)$

1982-02-20

Nagayoshi Iwahori , Takeo Yokonuma

On Some Generalization of B. Kostant’s Partition Function

1981-01-01

Ichirô Amemiya , Nagayoshi Iwahori , Kazuhiko Koike

In this note we shall show some useful properties of the partition function given by B. Kostant [1] associated to complex semi-simple Lie algebras. Some of these properties are shown … In this note we shall show some useful properties of the partition function given by B. Kostant [1] associated to complex semi-simple Lie algebras. Some of these properties are shown to be valid also for some generalized versions of Kostant's partition function (see Theorem 1 below). As an application of these properties we give (Theorem 4) an explicit formula for the multiplicity of the zero-weight in a given irreducible representation of the simple Lie algebra of type (G2).

On a conjecture of L. Solomon

1977-12-24

Shigeo Kusuoka , Nagayoshi Iwahori

Characterizations of linear groups of low rank

1976-12-15

Kensaku Gomi , Nagayoshi Iwahori

On a characterization of a class of functions defined on the space of positive definite matrices : Dedicated to Professor Shigeru Furuya on his 60th birthday

1977-10-30

Nagayoshi Iwahori

Non-representability of real general linear groups in higher dimensional lorentz groups

1952-08-01

Nagayoshi Iwahori

A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups

1965-01-01

Nagayoshi Iwahori , Takeshi Kondo

Some Topics on Coxeter Groups and Weyl Groups

1982-01-01

Nagayoshi Iwahori

On self-dual, completely reducible finite subgroups of $GL (2, k)$

1982-02-20

Nagayoshi Iwahori , Takeo Yokonuma

Some Topics on Coxeter Groups and Weyl Groups

1982-01-01

Nagayoshi Iwahori

On Some Generalization of B. Kostant’s Partition Function

1981-01-01

Ichirô Amemiya , Nagayoshi Iwahori , Kazuhiko Koike

On a conjecture of L. Solomon

1977-12-24

Shigeo Kusuoka , Nagayoshi Iwahori

On a characterization of a class of functions defined on the space of positive definite matrices : Dedicated to Professor Shigeru Furuya on his 60th birthday

1977-10-30

Nagayoshi Iwahori

Characterizations of linear groups of low rank

1976-12-15

Kensaku Gomi , Nagayoshi Iwahori

On primitive permutation groups of degree $2p=4q+2$ , p and q being prime numbers

1975-03-25

Izumi Miyamoto , Nagayoshi Iwahori

A characterization of odd order extensions of the Ree groups ${}^2F_4(q)$

1975-03-25

Ken-ichi Shinoda , Nagayoshi Iwahori

The conjugacy classes of the finite Ree groups of type$(F_4)$

1975-03-25

Ken-ichi Shinoda , Nagayoshi Iwahori

The conjugacy classes of Chevalley groups of type $(F_4)$ over finite fields of characteristic $p\ne 2$

1974-03-30

Toshiaki Shoji , Nagayoshi Iwahori

On a set of generating relations of the full transformation semigroups

1974-03-01

Nagayoshi Iwahori , Nobuko Iwahori

Centralizers of involutions in finite Chevalley groups

1970-01-01

Nagayoshi Iwahori

Seminar on Algebraic Groups and Related Finite Groups

1970-01-01

Armand Borel , Rayna J. Carter , C. W. Curtis +3 more

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A duality theorem for homogeneous manifolds of compact Lie groups

1966-06-01

Nagayoshi Iwahori , Mitsuo Sugiura

Generalized Tits system (Bruhat decompostition) on 𝑝-adic semisimple groups

1966-01-01

Nagayoshi Iwahori

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On some bruhat decomposition and the structure of the hecke rings of p-Adic chevalley groups

1965-12-01

Nagayoshi Iwahori , Hisatake Matsumoto

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A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups

1965-04-01

Nagayoshi Iwahori , Takeshi Kondo

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A criterion for the existence of a non-trivial partition of a finite group with applications to finite reflection groups

1965-01-01

Nagayoshi Iwahori , Takeshi Kondo

The space of $\mathfrak{p}$ -adic normsnorms

1963-01-01

Oscar Goldman , Nagayoshi Iwahori

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On Real Irreducible Representations of Lie Algebras

1959-02-01

Nagayoshi Iwahori

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Some remarks on tensor invariants of $O(\mathfrak{n}),$ $U(n), Sp(n)$ .

1958-04-01

Nagayoshi Iwahori

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An Extension of Tannaka Duality Theorem for Homogeneous Spaces

1958-01-01

Nagayoshi Iwahori , Nobuko Iwahori

Non-representability of real general linear groups in higher dimensional lorentz groups

1952-08-01

Nagayoshi Iwahori

On Cartan subalgebras of a Lie algebra

1950-01-01

Nagayoshi Iwahori , Ichirō Satake

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Coauthor	Papers Together
Nobuko Iwahori	2
Ken-ichi Shinoda	2
Takeshi Kondo	2
Takeo Yokonuma	1
Oscar Goldman	1
Kazuhiko Koike	1
Ichirô Amemiya	1
Kensaku Gomi	1
Hisatake Matsumoto	1
Mitsuo Sugiura	1
Toshiaki Shoji	1
Armand Borel	1
C. W. Curtis	1
T. A. Springer	1
Shigeo Kusuoka	1
Rayna J. Carter	1
Richard H. Steinberg	1
Ichirō Satake	1
Izumi Miyamoto	1

Les sous-groupes fermés de rang maximum des groupes de Lie clos

1949-12-01

Armand Borel , Jean Siebenthal

Quadratische Formen und orthogonale Gruppen

1974-01-01

Martin Eichler

Lectures on Chevalley Groups

2016-12-20

Robert Steinberg

The algebraic theory of semigroups

1964-01-01

A. H. Clifford , G. B. Preston

This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in … This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into the theories of minimal ideals in a semi group, inverse semi groups, simple semi groups, congruences on a semi group, and the embedding of a semi group in a group. Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semi group by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semi groups, J. M. Howie's theory of amalgamated free products of semi groups, and E. J. Tully's theory of representations of a semi group by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semi group.

La géométrie des groupes simples

1927-12-01

Élie Cartan

Representations of Coxeter groups and Hecke algebras

1979-06-01

David Kazhdan , G. Lusztig

Einfache Partitionen nicht-einfacher Gruppen

1961-12-01

Reinhold Baer

On a finite group with a partition

1961-12-01

Michio Suzuki

Nicht-einfache Partitionen endlicher Gruppen

1961-12-01

Otto H. Kegel

Sur certains groupes simples

1955-01-01

Catherine Chevalley

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Aufzählung der Partitionen endlicher Gruppen mit trivialer Fittingscher Untergruppe

1961-12-01

Otto H. Kegel

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Einfache Partitionen endlicher Gruppen mit nicht-trivialer Fittingscher Untergruppe

1961-12-01

Reinhold Baer

On algebraic Lie algebras.

1948-09-01

Morikuni Gotô

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Sur les groupes de Chevalley.

1958-07-01

Par Takashi ONO

Sur les groupes de Chevalley.Par Takashi ONO (Regu le 18 avril Sur les groupes de Chevalley.Par Takashi ONO (Regu le 18 avril

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The space of $\mathfrak{p}$ -adic normsnorms

1963-01-01

Oscar Goldman , Nagayoshi Iwahori

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Zur Struktur endlicher Gruppen mit nicht-trivialer Partition

1961-12-01

Otto H. Kegel , G. E. Wall

Invariant tensors under the real representation of unitary group and their applications.

1958-04-01

Tetsuzo Fukami

Invariant tensors under the real representation of unitary group and their applications. Invariant tensors under the real representation of unitary group and their applications.

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Cohomology theory of Lie groups and Lie algebras

1948-01-01

Claude Chevalley , Samuel Eilenberg

Russian with German summary.)(•) In LG, only analytic manifolds were considered.The definitions can be slightly modified in order to allow us to treat the case of manifolds of class Ck(k … Russian with German summary.)(•) In LG, only analytic manifolds were considered.The definitions can be slightly modified in order to allow us to treat the case of manifolds of class Ck(k ä 1).These modifications are trivial except as regards the definition of tangent vectors.This definition should be formulated as follows in the case of manifolds M of class C*.Let m be any point of M and let A be the class

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Über eine Beziehung zwischen geschlossenen Lie'schen Gruppen und diskontinuierlichen Bewegungsgruppen euklidischer Räume und ihre Anwendung auf die Aufzählung der einfachen Lie'schen Gruppen

1941-12-01

Eduard Stiefel

The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1

1935-01-01

H. S. M. Coxeter

On spherical functions over $\mathfrak{p}$-adic fields

1962-01-01

Ichirō Satake

A o-adic analogue of the spherical function was first considered by Mautner ) in the case of PLy. and then by Tamagawa ) for GLn over any o-adic division algebra.The … A o-adic analogue of the spherical function was first considered by Mautner ) in the case of PLy. and then by Tamagawa ) for GLn over any o-adic division algebra.The purpose of the present note is to show that the main part of the theory holds more generally under certain conditions, which are satisfied by almost all classical simple groups.It happenecl that similar considerations were con- rained in an independent work of Bruhat. )1. Notations and Assumptions.Let k be a o-adic number field.We denote by and =() the valuation ring in k and its unique prime ideal, respectively, z denoting a prime element.Let G be an algebraic subgroup of GLn(k), definecl over k, and set as follows:

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Sur les Representations des Groups Classiques -Adiques I

1961-04-01

François Bruhat

On the ζ-Functions of a Division Algebra

1963-03-01

Tsuneo Tamagawa

In this paper, we will develop a theory of C-functions with characters in a division algebra. The ordinary C-function of a division algebra was introduced by K. Hey [4], and … In this paper, we will develop a theory of C-functions with characters in a division algebra. The ordinary C-function of a division algebra was introduced by K. Hey [4], and generalized by M. Eichler [1] to L-functions with abelian characters. The first attempt to generalize these theories to C-functions with non-abelian characters is due to H. Maass [5]. Later, R. Godement [2] gave a method to get the most general formulations on these matters. In this note, we will define a type of C-functions of a division algebra over an algebraic number field which are included in Godement's work as a special case, and for which one can develop the theory of Euler products. The latter theory has its own meaning as an application of the theory of spherical functions on p-adic algebraic groups. Here we have a generalization of Hecke's theory of so-called Heckeoperators. (Theorem 1-6). One can expect that there exist similar theories for other simple algebraic groups defined over p-adic number fields, and that there will be applications of these theories to non-commutative number theory. The author wishes to express his thanks to Professor Shimura for some valuable suggestions about the first part of this paper.

An Algebraic Proof of a Property of Lie Groups

1941-10-01

Claude Chevalley

An Extension of Tannaka Duality Theorem for Homogeneous Spaces

1958-01-01

Nagayoshi Iwahori , Nobuko Iwahori

A formula for the multiplicity of a weight

1959-01-01

Bertram Kostant

53(5) This is 53(5) This is

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An application of the Morse theory to the topology of Lie-groups

1956-01-01

Raoul Bott

This paper is primarily devoted to a detailed account of the results announced and sketched in [5 |.It will be followed by a joint paper witli H. SAMELSON on the … This paper is primarily devoted to a detailed account of the results announced and sketched in [5 |.It will be followed by a joint paper witli H. SAMELSON on the loop-space of symmetric spaces in general.We recall the principal results of [3].Let G be a compact Lie group; T'C G shall denote a torus in G and C( T) the centralizer of T in G.The space of loops on G is denoted by ^2(G).(For detailed definitions, see §9.) THEOREM A. -If G is a connected^ simply connected^ compact Lie groups then the spaces 12 (G) aud G/C( T') have the following properties : a.They are free of torsion; b.Their odd Betti numbers vanish; c.Their Betti numbers can be read off from the diagram of G. '25l> R. BOTT.THEOREM B. -1° The Poincare series of the loop-space, i2(G'), is given by P(^(G),t)=^t^\where A runs over the cells of the fundamental chamber ^.2° If^y is a lattice point ofF in t, and if C(^Y) is the centralize r of the direction JT, then the Poincare series of G/C(A^) is given bywhere now the summation is extended over the cells of 5 7 which contain X in their closure.As every C(7'' / ) is conjugate to some C(^T), ^T^r, part 2° of this theorem describes the homology of all the spaces G/C(T').It also relates their Poincare series to that of^(G).These formulae can of course be expressed entirely in terms of the rootforms of G on t : Let { 0; \rj (i' = i, . .., /n), denote the root-forms on t which take positive values in 5 7 '.Also let H^ denote the Weyl group ofG in t.Finally, ifJTet, define a function ^*, on W by : A* (w) == number of the root-forms j 6^-J£F whose values at X and w'A" differ in sign.Thus, A *(w) == number of planes of the infinitesimal diagram D'\ crossed by the line from X to w'X.Finally let p(^T) denote the order of the subgroup of W which leaves JT fixed.In terms of these notions, theorem B is equivalent to : THEOREM B'. -i° The Poincare series of^l(G) is given by " 2^[8,W] P^(G)^t)=---j t^ dv, I A 1 ŵhere the integral is taken overly \ A | denotes the volume of a fundamental cell o/Z), and [a] denotes the greatest integer less than a; 2° The Poincare series of G/C(^T), X arbitrary in t, is given by P{(G/CW);t}^--.^t^.w€Î n particular (for X in ^) the iq^ Betti number of G/T is equal to the

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Quadratische Formen und Orthogonale Gruppen

1952-01-01

Martin Eichler

Cohomologie Galoisienne

1965-01-01

Jean-Pierre Serre

A Proof of Tannaka Duality Theorem

1958-01-01

Nobuko Iwahori

On the Compacity of the Orthogonal Groups

1954-06-01

Takashi Ono

It is a well known fact on Lorenz groups that a quadratic form f is definite if and only if the corresponding orthogonal group O n (R ∞ , f … It is a well known fact on Lorenz groups that a quadratic form f is definite if and only if the corresponding orthogonal group O n (R ∞ , f ) where R ∞ is the real number field, is compact. In this note, we shall show that the analogue of this holds for the case of the p -adic orthogonal group O n (R p , f ), where R p is the rational p -adic number field, as a special result of the more general statement on the completely valued fields.

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Théorème de Bruhat et sous-groupes paraboliques

1962-01-01

Jacques Tits