Analytic Continuation of Equivariant Distributions

Abstract We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein’s theory of analytic continuation of holonomic distributions. We use this to construct H-equivariant functio...

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Bibliographic Details
Published in:International mathematics research notices 2019-12, Vol.2019 (23), p.7160-7192
Main Authors: Gourevitch, Dmitry, Sahi, Siddhartha, Sayag, Eitan
Format: Article
Language:English
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Summary:Abstract We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein’s theory of analytic continuation of holonomic distributions. We use this to construct H-equivariant functionals on principal series representations of G, where G is a real reductive group and H is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on principal series representations and of analytic continuation of standard intertwining operators. Finally, we extend our constructions to the p-adic case using a recent result of Hong and Sun.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnx326