Unitary representations of maximal parabolic subgroups of the classical groups

1976 ◽  
Vol 8 (180) ◽  
pp. 0-0 ◽  
Author(s):  
Joseph A. Wolf
Keyword(s):  
Unitary Representations ◽  
Classical Groups ◽  
Parabolic Subgroups ◽  
Maximal Parabolic Subgroups

On Certain Classes of Unitary Representations for Split Classical Groups

2007 ◽  
Vol 59 (1) ◽  
pp. 148-185 ◽  
Author(s):  
Goran Muić
Keyword(s):  
Unitary Representations ◽  
Classical Groups ◽  
Parabolic Subgroups

AbstractIn this paper we prove the unitarity of duals of tempered representations supported onminimal parabolic subgroups for split classical p-adic groups. We also construct a family of unitary spherical representations for real and complex classical groups.

Residues of standard intertwining operators on p-adic classical groups

2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Xiaoxiang Yu
Keyword(s):  
Intertwining Operators ◽  
Classical Groups ◽  
Parabolic Subgroups ◽  
Supercuspidal Representations ◽  
Maximal Parabolic Subgroups

AbstractWe study two basic problems involved in the study of the standard intertwining operators attached to representations induced from irreducible unitary supercuspidal representations on maximal parabolic subgroups of

scholarly journals Tight Quotients and Double Quotients in the Bruhat Order

10.37236/1871 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
John R. Stembridge
Keyword(s):  
Coxeter Groups ◽  
Upper Bounds ◽  
Bruhat Order ◽  
Weyl Groups ◽  
Order Dimension ◽  
Parabolic Subgroups ◽  
Affine Weyl Groups ◽  
Positive Side ◽  
Maximal Parabolic Subgroups

It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by projecting onto two-sided (i.e., "double") quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be represented as an orbit in the reflection representation, and each double quotient corresponds to the portion of an orbit on the positive side of certain hyperplanes. In some cases, these orbit representations are "tight" in the sense that the root system induces an ordering on the orbit that yields effective coordinates for the Bruhat order, and hence also provides upper bounds for the order dimension. In this paper, we (1) provide a general characterization of tightness for one-sided quotients, (2) classify all tight one-sided quotients of finite Coxeter groups, and (3) classify all tight double quotients of affine Weyl groups.

scholarly journals Eisenstein Series Arising from Jordan Algebras

2019 ◽  
Vol 72 (1) ◽  
pp. 183-201 ◽  
Author(s):  
Marcela Hanzer ◽  
Gordan Savin
Keyword(s):  
Eisenstein Series ◽  
Jordan Algebra ◽  
Jordan Algebras ◽  
Algebra Structure ◽  
Parabolic Subgroups ◽  
Automorphic Representations ◽  
Unipotent Radicals ◽  
Maximal Parabolic Subgroups

AbstractWe describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

The Plancherel formula for parabolic subgroups of the classical groups

1978 ◽  
Vol 34 (1) ◽  
pp. 120-161 ◽  
Author(s):  
Ronald L. Lipsman ◽  
Joseph A. Wolf
Keyword(s):  
Plancherel Formula ◽  
Classical Groups ◽  
Parabolic Subgroups
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