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Distinguished Representations for Quadratic Extensions

Published online by Cambridge University Press:  04 December 2007

DIPENDRA PRASAD
DIPENDRA PRASAD
Affiliation:
Mehta Research Institute, Chhatnag Road, Jhusi, Allahabad-211019, India; e-mail: [email protected]
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Abstract

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Let K be a quadratic extension of a field k which is either local field or a finite field. Let G be an algebraic group over k. The aim of the present paper is to understand when a representation of G(K) has a G(k) invariant linear form. We are able to accomplish this in the case when G is the group of invertible elements of a division algebra over k of odd index if k is a local field, and for general connected groups over finite fields.

Keywords

distinguished representationsShintani descentcharacter identityWeyl integration formulaLang‘s theoremfunctorial lift.
Type
Research Article
Information
Compositio Mathematica , Volume 119 , Issue 3 , December 1999 , pp. 335 - 345
Copyright
© 1999 Kluwer Academic Publishers