scholarly journals The Langlands Classification of Representations Having Integral Regular Infinitesimal Characters of the Classical Groups of TypeAn,Bn, andCn

1997 ◽  
Vol 192 (1) ◽  
pp. 14-42
Author(s):  
Zhao Qiang ◽  
Hou Zixin
Keyword(s):  
Classical Groups

scholarly journals On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal and symplectic groups

1995 ◽  
Vol 58 (2) ◽  
pp. 232-247 ◽  
Author(s):  
S. P. Glasby
Keyword(s):  
Cyclic Group ◽  
Projective Representation ◽  
Faithful Representation ◽  
Explicit Description ◽  
Symplectic Groups ◽  
Classical Groups ◽  
Central Extensions ◽  
Central Product ◽  
Extraspecial Group

AbstractIf R is a 2-group of symplectic type with exponent 4, then R is isomorphic to the extraspecial group , or to the central product 4 o 21+2n of a cyclic group of order 4 and an extraspecial group, with central subgroups of order 2 amalgamated. This paper gives an explicit description of a projective representation of the group A of automorphisms of R centralizing Z(R), obtained from a faithful representation of R of degree 2n. The 2-cocycle associated with this projective representation takes values which are powers of −1 if R is isomorphic to and powers of otherwise. This explicit description of a projective representation is useful for computing character values or computing with central extensions of A. Such central extensions arise naturally in Aschbacher's classification of the subgroups of classical groups.

A note on powers in simple groups

1997 ◽  
Vol 122 (1) ◽  
pp. 91-94 ◽  
Author(s):  
JAN SAXL ◽  
JOHN S. WILSON
Keyword(s):  
Conjugacy Class ◽  
Simple Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Classical Groups ◽  
Similar Combination

In [7], the second author proved that there is an integer k such that every element of a finite non-abelian simple group S is a product of k commutators in S. The motivation for proving this result came from a model-theoretic question about simple groups. The proof depended on the classification of the finite simple groups, a theorem of Malle, Saxl and Weigel [5] which shows that in many finite simple classical groups S there is a real conjugacy class R such that S=R3∪{1}, and an ultraproduct argument. Here we shall use a similar combination of ideas to prove the following result.

Discrete Series for p-adic SO(2n) and Restrictions of Representations of O(2n)

2011 ◽  
Vol 63 (2) ◽  
pp. 327-380 ◽  
Author(s):  
Chris Jantzen
Keyword(s):  
Discrete Series ◽  
The Other ◽  
Classical Groups

Abstract In this paper we give a classification of discrete series for SO(2n, F), F p-adic, similar to that of Mœglin–Tadić for the other classical groups. This is obtained by taking the Mœglin–Tadić classification for O(2n, F) and studying how the representations restrict to SO(2n, F). We then extend this to an analysis of how admissible representations of O(2n, F) restrict.

scholarly journals Whittaker unitary dual of affine graded Hecke algebras of type E

2009 ◽  
Vol 145 (6) ◽  
pp. 1563-1616 ◽  
Author(s):  
Dan Barbasch ◽  
Dan Ciubotaru
Keyword(s):  
Hecke Algebras ◽  
Classical Groups ◽  
Unitary Spectrum ◽  
Unitary Dual ◽  
Appl Math ◽  
Graded Hecke Algebras

AbstractThis paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori–Matsumoto involution, this is also equivalent to the classification of the spherical unitary dual for type E. Together with some results of Barbasch and Moy (D. Barbasch and A. Moy, Unitary spherical spectrum for p-adic classical groups, Acta Appl. Math. 44 (1996), 3–37; D. Barbasch, The spherical unitary spectrum of split classical real and p-adic groups, Preprint (2006), math/0609828) and Ciubotaru (D. Ciubotaru, The Iwahori spherical unitary dual of the split group of type F4, Represent. Theory 9 (2005), 94–137), this work completes the classification of the Whittaker Iwahori-spherical unitary dual or, equivalently, the spherical unitary dual of any split p-adic group.

On the classification of the classical groups

1967 ◽  
Vol 97 (1) ◽  
pp. 66-76 ◽  
Author(s):  
A. Wagner
Keyword(s):  
Classical Groups
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