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Zentralblatt MATH Database 1931 2009 c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
 

Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Zbl 1079.22013
Anandavardhanan, U.K.
Distinguished non-Archimedean representation. (English)
Tandon, Rajat (ed.), Algebra and number theory. Proceedings of the silver jubilee
conference, Hyderabad, India, December 1116, 2003. New Delhi: Hindustan Book
Agency. 183-192 (2005). ISBN 81-85931-57-7/hbk
This expository article reviews definitions and results on irreducible admissible repre-
sentations of a p-adic group G which have a nonzero linear form invariant under a
subgroup H fixed by an involution. Various results are known when G is GL(n, E) and
H is GL(n, F), where E is a quadratic extension of F, and for analogous pairs. The au-
thor reports on his study with D. Prasad of such on G = SL(n, E) with H = SL(n, F),
and it is that dimCHomH(, 1) 1 for odd n, but that the multiplicity might be bigger
than 1 when n is even, even when is cuspidal.
Yuval Z. Flicker (Columbus)
Keywords : distinguished non-archimedean representations; Gelfand pairs
Classification :
22E50 Repres. of Lie and linear algebraic groups over local fields
11F70 Representation-theoretic methods in automorphic theory

  

Source: Anandavardhanan, U. K. - Department of Mathematics, Indian Institute of Technology Bombay

 

Collections: Mathematics