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By A. L. Onishchik and E. B. Vinberg (translated from the Russian by D. A. Leites): 328 pp., DM.128.–, ISBN 3 540 50614 4 (Springer, 1990).
By A. L. Onishchik and E. B. Vinberg (translated from the Russian by D. A. Leites): 328 pp., DM.128.–, ISBN 3 540 50614 4 (Springer, 1990).
By Melvin Hausner & Jacob T. Schwartz: pp. x, 229; £5.15s. (Thomas Nelson & Sons Ltd., London, 1968).
By Melvin Hausner & Jacob T. Schwartz: pp. x, 229; £5.15s. (Thomas Nelson & Sons Ltd., London, 1968).
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By G. Higman and M. B. Powell: pp. xii, 327. £6. (Academic Press Inc.,(London)Ltd., London, 1971.)
By G. Higman and M. B. Powell: pp. xii, 327. £6. (Academic Press Inc.,(London)Ltd., London, 1971.)
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
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By Francois Digne and Jean Michel: 159 pp., £11.95, LMS Members' price £8.95, ISBN 0 521 40648 X (Cambridge University Press, 1991).
By Francois Digne and Jean Michel: 159 pp., £11.95, LMS Members' price £8.95, ISBN 0 521 40648 X (Cambridge University Press, 1991).
We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces.In high rank we obtain a complete classification.In rank one, we obtain some partial …
We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces.In high rank we obtain a complete classification.In rank one, we obtain some partial results and give a conjectural picture.
Let [Formula: see text] be a group and [Formula: see text] be an automorphism of [Formula: see text]. Two elements [Formula: see text] are said to be [Formula: see text]-twisted …
Let [Formula: see text] be a group and [Formula: see text] be an automorphism of [Formula: see text]. Two elements [Formula: see text] are said to be [Formula: see text]-twisted conjugate if [Formula: see text] for some [Formula: see text]. We say that a group [Formula: see text] has the [Formula: see text]-property if the number of [Formula: see text]-twisted conjugacy classes is infinite for every automorphism [Formula: see text] of [Formula: see text]. In this paper, we prove that twisted Chevalley groups over a field [Formula: see text] of characteristic zero have the [Formula: see text]-property as well as the [Formula: see text]-property if [Formula: see text] has finite transcendence degree over [Formula: see text] or [Formula: see text] is periodic.
We study the moduli space of principally polarized abelian varieties over fields of positive characteristic. In this paper we describe certain unions of Ekedahl-Oort strata contained in the supersingular locus …
We study the moduli space of principally polarized abelian varieties over fields of positive characteristic. In this paper we describe certain unions of Ekedahl-Oort strata contained in the supersingular locus in terms of Deligne-Lusztig varieties. As a corollary we show that each Ekedahl-Oort stratum contained in the supersingular locus is reducible except possibly for small <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.
Abstract A subgroup H of a group G is said to be pronormal in G if H and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>H</m:mi> <m:mi>g</m:mi> </m:msup> </m:math> {H^{g}} are conjugate in <m:math …
Abstract A subgroup H of a group G is said to be pronormal in G if H and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>H</m:mi> <m:mi>g</m:mi> </m:msup> </m:math> {H^{g}} are conjugate in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">〈</m:mo> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:msup> <m:mi>H</m:mi> <m:mi>g</m:mi> </m:msup> <m:mo stretchy="false">〉</m:mo> </m:mrow> </m:math> {\langle H,H^{g}\rangle} for every <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>g</m:mi> <m:mo>∈</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> {g\in G} . In this paper, we determine the finite simple groups of type <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>E</m:mi> <m:mn>6</m:mn> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>q</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {E_{6}(q)} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mmultiscripts> <m:mi>E</m:mi> <m:mn>6</m:mn> <m:none /> <m:mprescripts /> <m:none /> <m:mn>2</m:mn> </m:mmultiscripts> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>q</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.
This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the $1+1+16=18$ families of finite simple …
This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the $1+1+16=18$ families of finite simple groups, as an introduction to the sporadic groups. These are described next, in three levels of increasing complexity, plus the six isolated "pariah" groups. The (old) five Mathieu groups make up the first, smallest order level. The seven groups related to the Leech lattice, including the three Conway groups, constitute the second level. The third and highest level contains the Monster group $\mathbb M$, plus seven other related groups. Next a brief mention is made of the remaining six pariah groups, thus completing the $5+7+8+6=26$ sporadic groups. The review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every …
Every conic symplectic singularity admits a universal Poisson deformation and a universal filtered quantization, thanks to the work of Losev and Namikawa. We begin this paper by showing that every such variety admits a universal equivariant Poisson deformation and a universal equivariant quantization with respect to a reductive group acting on it by \mathbb{C}^\times -equivariant Poisson automorphisms. We go on to study these definitions in the context of nilpotent Slodowy slices. First, we give a complete description of the cases in which the finite W -algebra is a universal filtered quantization of the slice, building on the work of Lehn–Namikawa–Sorger. This leads to a near-complete classification of the filtered quantizations of nilpotent Slodowy slices. The subregular slices in non-simply laced Lie algebras are especially interesting: with some minor restrictions on Dynkin type, we prove that the finite W -algebra is a universal equivariant quantization with respect to the Dynkin automorphisms coming from the unfolding of the Dynkin diagram. This can be seen as a non-commutative analogue of Slodowy's theorem. Finally, we apply this result to give a presentation of the subregular finite W -algebra of type \mathsf{B} as a quotient of a shifted Yangian.
An orthogonal basis in root space, related to the weights of the smallest representation, is used to provide a list of the algebraic conditions which the structure constants Nαβ must …
An orthogonal basis in root space, related to the weights of the smallest representation, is used to provide a list of the algebraic conditions which the structure constants Nαβ must satisfy for all simple Lie algebras. A particular explicit set of solutions for all the Nαβ is given.