scholarly journals Degenerate principal series for classical and odd GSpin groups in the general case

2020 ◽  
Vol 24 (14) ◽  
pp. 403-434
Author(s):  
Yeansu Kim ◽  
Baiying Liu ◽  
Ivan Matić
Keyword(s):  
Principal Series ◽  
Degenerate Principal Series

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

scholarly journals Analytic Continuation of Equivariant Distributions

2018 ◽  
Vol 2019 (23) ◽  
pp. 7160-7192 ◽  
Author(s):  
Dmitry Gourevitch ◽  
Siddhartha Sahi ◽  
Eitan Sayag
Keyword(s):  
Analytic Continuation ◽  
Reductive Group ◽  
Principal Series ◽  
Real Algebraic Varieties ◽  
Series Representations ◽  
Degenerate Principal Series ◽  
Special Case ◽  
Adic Case ◽  
Principal Series Representations ◽  
Whittaker Models

Abstract We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein’s theory of analytic continuation of holonomic distributions. We use this to construct H-equivariant functionals on principal series representations of G, where G is a real reductive group and H is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on principal series representations and of analytic continuation of standard intertwining operators. Finally, we extend our constructions to the p-adic case using a recent result of Hong and Sun.

Sign in / Sign up

Export Citation Format

Share Document