 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1079.22013
Anandavardhanan, U.K.
Distinguished nonArchimedean 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. 183192 (2005). ISBN 8185931577/hbk
This expository article reviews definitions and results on irreducible admissible repre
sentations of a padic 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 nonarchimedean representations; Gelfand pairs
Classification :
22E50 Repres. of Lie and linear algebraic groups over local fields
11F70 Representationtheoretic methods in automorphic theory
