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Distinguished non-Archimedean representations

U. K. Anandavardhanan
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Abstract

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation πof G. In particular an important question is whether or not the dimension of this space is bounded by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When $n$ is even, the space of H-invariant forms on πcan have dimension more than one even when πis supercuspidal. The latter work is joint with Dipendra Prasad.

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U. K. Anandavardhanan. 2004-12-23. Distinguished non-Archimedean representations. https://arxiv.org/abs/math/0412471

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