SU\G(𝔸)/K·U

Discrete series for semisimple Lie groups. II: Explicit determination of the characters

Harish-chandra Harish-Chandra

Type: Article

Publication Date: 1966-01-01

Citations: 413

DOI: https://doi.org/10.1007/bf02392813

Abstract

Let G be a connected semisimple Lie group and K a maximal compact subgroup of G.We shall show in this paper that G has a discrete series (see [4 (d), w 5]) ff and only if it has a compact Cartan subgroup B. Let Ea denote the set of all equivalence classes of irreducible unitary representations of G, wMch are square-integrable.For any ~o E ~a, let | denote the character, X~ the infinitesimal character and d(r the formal degree (see [4 (d), w 3]) of co.Then it is known [4 (d), w 5] that the distribution

Locations

Similar Works

Action Title Year Authors
+ Character formulas for the discrete series for semisimple Lie groups 1979 Takeshi Hirai
+ PDF Chat A character formula for the discrete series of a semisimple Lie group 1980 Jorge Vargas
+ PDF Chat Character formulas for discrete series on semisimple Lie groups 1976 Rebecca A. Herb
+ Explicit form of the characters of discrete series representations of semisimple Lie groups 1973 Takeshi Hirai
+ PDF Chat The characters of the discrete series for semisimple Lie groups 1981 Takeshi Hirai
+ The theory of characters and the discrete series for semisimple Lie groups 1973 V. S. Varadarajan
+ PDF Chat On the characters of the averaged discrete series representations of semisimple Lie groups 1983 Shunsuke Mikami
+ PDF Chat The characters of the holomorphic discrete series 1975 S. Martens
+ PDF Chat Discrete series for semisimple Lie groups I: Construction of invariant eigendistributions 1965 Harish-chandra Harish-Chandra
+ Discrete Series for Semisimple Lie Groups. II 1984 Harish-chandra Harish-Chandra
+ On an Infinitesimal Characterization of the Discrete Series 1975 Thomas J. Enright
V. S. Varadarajan
+ PDF Chat Character identities and asymptotic behavior of matrix coefficients of discrete series 1986 Henryk Hecht
Dragan Miličić
+ Description of the Associated Varieties for the Discrete Series Representations of a Semisimple Lie Group 1998 Hiroshi Yamashita
+ Discrete Series for Semisimple Lie Groups I 1984 Harish-chandra Harish-Chandra
+ The Discrete Series for a Semisimple Symmetric Space 1986 Mogens Flensted–Jensen
+ PDF Chat A geometric construction of the discrete series for semisimple Lie groups 1979 Michael Atiyah
Wilfried Schmid
+ The characters of discrete series as orbital integrals 1976 James Arthur
+ A geometric construction of the discrete series for semisimple Lie groups 1977 Michael Atiyah
Wilfried Schmid
+ A Geometric Construction of the Discrete Series for Semisimple Lie Groups 1977 Michael Atiyah
Wilfried Schmid
+ Character polynomials of discrete series representations 1981 Donald R. King

Works That Cite This (387)

Action Title Year Authors
+ PDF Chat Functional equations of Selberg and Ruelle zeta functions for non-unitary twists 2020 Polyxeni Spilioti
+ PDF Chat Parabolic Verma Modules and Invariant Differential Operators 2020 V. K. Dobrev
+ On the meromorphic continuation of Eisenstein series 2022 Joseph Bernstein
Erez Lapid
+ A duality for symmetric spaces with applications to group representations 1970 Sigurđur Helgason
+ On the four Euclidean conformal group structure of the Sturmian operator 2008 Jean‐Pierre Gazeau
+ Composition Series and Intertwining Operators for the Spherical Principal Series. I 1977 Kenneth D. Johnson
Nolan R. Wallach
+ PDF Chat Invariant differential operators for non-compact Lie groups: The main su(n, n) cases 2013 V. K. Dobrev
+ Pointwise convergence of noncommutative Fourier series 2019 Guixiang Hong
Simeng Wang
Xumin Wang
+ PDF Chat Square Integrable Representations of Semisimple Lie Groups 1974 Juan Tirao
+ Intégrales orbitales semi-simples et centre de l'algèbre enveloppante 2019 Jean‐Michel Bismut
Shu Shen

Works Cited by This (28)

Action Title Year Authors
+ PDF Chat Discrete series for semisimple Lie groups I: Construction of invariant eigendistributions 1965 Harish-chandra Harish-Chandra
+ PDF Chat Hypermaximality of certain operators on Lie groups 1952 I. E. Segal
+ PDF Chat Representations of semisimple Lie groups. II 1954 Harish-chandra Harish-Chandra
+ PDF Chat Invariant eigendistributions on a semisimple Lie group 1965 Harish-chandra Harish-Chandra
+ Representations of Semisimple Lie Groups 1954 Harish-chandra Harish-Chandra
+ PDF Chat The Dimension of Spaces of Automorphic Forms 1963 R. P. Langlands
+ PDF Chat Representations of a semisimple Lie group on a Banach space. I 1953 Harish-chandra Harish-Chandra
+ PDF Chat Invariant eigendistributions on semisimple Lie groups 1963 Harish-chandra Harish-Chandra
+ PDF Chat Infinite-dimensional group representations 1963 George W. Mackey
+ Differential Geometry and Symmetric Spaces 2001 Sigurđur Helgason