scholarly journals Branching laws for discrete series of some affine symmetric spaces

2021 ◽  
Vol 17 (4) ◽  
pp. 1291-1320
Author(s):  
Bent Ørsted ◽  
Birgit Speh
Keyword(s):  
Symmetric Spaces ◽  
Discrete Series ◽  
Branching Laws ◽  
Affine Symmetric Spaces

CORWIN–GREENLEAF MULTIPLICITY FUNCTIONS FOR HERMITIAN SYMMETRIC SPACES AND MULTIPLICITY-ONE THEOREM IN THE ORBIT METHOD

2010 ◽  
Vol 21 (03) ◽  
pp. 279-296 ◽  
Author(s):  
SALMA NASRIN
Keyword(s):  
Classical Limit ◽  
Symmetric Spaces ◽  
Discrete Series ◽  
Coadjoint Orbit ◽  
Symmetric Pair ◽  
Orbit Method ◽  
Hermitian Symmetric Spaces ◽  
Branching Laws ◽  
Scalar Type ◽  
Multiplicity Free

Kobayashi's multiplicity-free theorem asserts that irreducible unitary highest-weight representations π are multiplicity-free when restricted to every symmetric pair if π is of scalar type. The aim of this paper is to find the "classical limit" of this multiplicity-free theorem in terms of the geometry of two coadjoint orbits, for which the correspondence is predicted by the Kirillov–Kostant–Duflo orbit method.For this, we study the Corwin–Greenleaf multiplicity function [Formula: see text] for Hermitian symmetric spaces G/K. First, we prove that [Formula: see text] for any G-coadjoint orbit [Formula: see text] and any K-coadjoint orbit [Formula: see text] if [Formula: see text]. Here, 𝔤 = 𝔨 + 𝔭 is the Cartan decomposition of the Lie algebra 𝔤 of G.Second, we find a necessary and sufficient condition for [Formula: see text] by means of strongly orthogonal roots. This criterion may be regarded as the "classical limit" of a special case of the Hua–Kostant–Schmid–Kobayashi branching laws of holomorphic discrete series representations with respect to symmetric pairs.

scholarly journals Orbits on affine symmetric spaces under the action of the isotropy subgroups

1980 ◽  
Vol 32 (2) ◽  
pp. 399-414 ◽  
Author(s):  
Toshio OSHIMA ◽  
Toshihiko MATSUKI
Keyword(s):  
Symmetric Spaces ◽  
Affine Symmetric Spaces

scholarly journals K-invariant cusp forms for reductive symmetric spaces of split rank one

2019 ◽  
Vol 31 (2) ◽  
pp. 341-349
Author(s):  
Erik P. van den Ban ◽  
Job J. Kuit ◽  
Henrik Schlichtkrull
Keyword(s):  
Symmetric Spaces ◽  
Discrete Series ◽  
Series Representation ◽  
Compact Subgroup ◽  
Cusp Forms ◽  
Series Representations ◽  
Rank One ◽  
Discrete Series Representations ◽  
Generalized Matrix ◽  
Split Rank

AbstractLet {G/H} be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for {G/H}. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of {G/H}.

scholarly journals On affine symmetric spaces

1965 ◽  
Vol 119 (2) ◽  
pp. 291-291 ◽  
Author(s):  
Sebastian S. Koh
Keyword(s):  
Symmetric Spaces ◽  
Affine Symmetric Spaces
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