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Distinguished non-Archimedean representations

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Algebra and Number Theory

Abstract

For a symmetric space (G, H), one is interested in understanding the vector space of H-invariant linear forms on a representation π of 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 = RE/FGL(n), H = GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G = RE/FSL(n),H = SL(n)) is a Gelfand pair when n is odd. When n is even, the space of H-invariant forms on π can have dimension more than one even when π is supercuspidal.

The later work is joint with Dipendra Prasad.

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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India

    U. K. Anandavardhanan

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  1. U. K. Anandavardhanan
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Hyderabad P.O. Central University, Hyderabad, 500 046, India

    Rajat Tandon

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© 2005 Hindustan Book Agency

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Anandavardhanan, U.K. (2005). Distinguished non-Archimedean representations. In: Tandon, R. (eds) Algebra and Number Theory. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-23-1_12

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