Embeddings of Discrete Series into Principal Series

1990 ◽  
pp. 147-175 ◽  
Author(s):  
Toshihiko Matsuki ◽  
Toshio Oshima
Keyword(s):  
Discrete Series ◽  
Principal Series

scholarly journals MORITA'S THEORY FOR THE SYMPLECTIC GROUPS

2011 ◽  
Vol 07 (08) ◽  
pp. 2115-2137 ◽  
Author(s):  
ZHI QI ◽  
CHANG YANG
Keyword(s):  
Symplectic Group ◽  
Discrete Series ◽  
Principal Series ◽  
Symplectic Groups ◽  
Holomorphic Discrete Series ◽  
Algebraic Interpretation ◽  
Series Representations ◽  
Discrete Series Representations ◽  
Principal Series Representations

We construct and study the holomorphic discrete series representations and the principal series representations of the symplectic group Sp (2n, F) over a p-adic field F as well as a duality between some sub-representations of these two representations. The constructions of these two representations generalize those defined in Morita and Murase's works. Moreover, Morita built a duality for SL (2, F) defined by residues. We view the duality we defined as an algebraic interpretation of Morita's duality in some extent and its generalization to the symplectic groups.

scholarly journals The embeddings of discrete series into principal series for an exceptional real simple Lie group of type $G_2$

1996 ◽  
Vol 36 (3) ◽  
pp. 557-595
Author(s):  
Tetsumi Yoshinaga ◽  
Hiroshi Yamashita
Keyword(s):  
Lie Group ◽  
Discrete Series ◽  
Principal Series

L-Functions for GSp(2) × GL(2): Archimedean Theory and Applications

2009 ◽  
Vol 61 (2) ◽  
pp. 395-426 ◽  
Author(s):  
Tomonori Moriyama
Keyword(s):  
Discrete Series ◽  
Series Representation ◽  
Principal Series ◽  
Algebraic Number Field ◽  
Automorphic Representation ◽  
Explicit Computation ◽  
Principal Series Representation ◽  
Cuspidal Automorphic Representation ◽  
Discrete Series Representation ◽  
Totally Real

Abstract. Let Π be a generic cuspidal automorphic representation of GSp(2) defined over a totally real algebraic number field k whose archimedean type is either a (limit of) large discrete series representation or a certain principal series representation. Through explicit computation of archimedean local zeta integrals, we prove the functional equation of tensor product L-functions L(s,Π × σ) for an arbitrary cuspidal automorphic representation σ of GL(2). We also give an application to the spinor L-function of Π.

Reducibility of Generalized Principal Series

2005 ◽  
Vol 57 (3) ◽  
pp. 616-647 ◽  
Author(s):  
Goran Muić
Keyword(s):  
Discrete Series ◽  
Principal Series

AbstractIn this paper we describe reducibility of non-unitary generalized principal series for classical p-adic groups in terms of the classification of discrete series due to Moeglin and Tadić.

scholarly journals Rodier type theorem for generalized principal series

2021 ◽  
Author(s):  
Caihua Luo
Keyword(s):  
Weyl Group ◽  
Coxeter Group ◽  
Structure Theorem ◽  
Borel Subgroup ◽  
Discrete Series ◽  
Type Theorem ◽  
Series Representation ◽  
Reductive Group ◽  
Principal Series ◽  
Levi Subgroup

AbstractGiven a regular supercuspidal representation $$\rho $$ ρ of the Levi subgroup M of a standard parabolic subgroup $$P=MN$$ P = M N in a connected reductive group G defined over a non-archimedean local field F, we serve you a Rodier type structure theorem which provides us a geometrical parametrization of the set $$JH(Ind^G_P(\rho ))$$ J H ( I n d P G ( ρ ) ) of Jordan–Hölder constituents of the Harish-Chandra parabolic induction representation $$Ind^G_P(\rho )$$ I n d P G ( ρ ) , vastly generalizing Rodier structure theorem for $$P=B=TU$$ P = B = T U Borel subgroup of a connected split reductive group about 40 years ago. Our novel contribution is to overcome the essential difficulty that the relative Weyl group $$W_M=N_G(M)/M$$ W M = N G ( M ) / M is not a coxeter group in general, as opposed to the well-known fact that the Weyl group $$W_T=N_G(T)/T$$ W T = N G ( T ) / T is a coxeter group. Along the way, we sort out all regular discrete series/tempered/generic representations for arbitrary G, generalizing Tadić’s work on regular discrete series representation for split $$(G)Sp_{2n}$$ ( G ) S p 2 n and $$SO_{2n+1}$$ S O 2 n + 1 , and also providing a new simple proof of Casselman–Shahidi’s theorem on generalized injectivity conjecture for regular generalized principal series. Indeed, such a beautiful structure theorem also holds for finite central covering groups.

Composition series of generalized principal series; the case of strongly positive discrete series

2004 ◽  
Vol 140 (1) ◽  
pp. 157-202 ◽  
Author(s):  
Goran Muić
Keyword(s):  
Discrete Series ◽  
Principal Series ◽  
Composition Series

PARTICLE CREATION AND UIRs OF DE SITTER GROUP

2008 ◽  
Vol 23 (21) ◽  
pp. 1793-1800
Author(s):  
SHAHPOOR MORADI
Keyword(s):  
Casimir Operator ◽  
Discrete Series ◽  
Particle Creation ◽  
Principal Series ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dirac Particles ◽  
Inequivalent Representations ◽  
Creation Rate

In this paper using the first Casimir operator of de Sitter group we obtain the field equations for spin-0 and spin-1/2 fields. After finding the exact solutions, we calculate the Bogoliubov coefficients and the particle creation rate for scalar and Dirac particles. Three series of inequivalent representations are distinguished for de Sitter group: the principal, complementary and discrete series. It is shown that only for principal series massive particles are produced. The thermal particle creation rate is compared with the previous results and it is shown that the results are the same.

scholarly journals The embeddings of discrete series into principal series for an exceptional real simple Lie group of type $G_2$

1996 ◽  
Vol 72 (4) ◽  
pp. 78-81
Author(s):  
Tetsumi Yoshinaga ◽  
Hiroshi Yamashita
Keyword(s):  
Lie Group ◽  
Discrete Series ◽  
Principal Series
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