Analytic Continuation of Equivariant Distributions

Dmitry Gourevitch, Siddhartha Sahi, Eitan Sayag

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)7160-7192
Number of pages33
JournalInternational Mathematics Research Notices
Volume2019
Issue number23
DOIs
StatePublished - 1 Dec 2019

ASJC Scopus subject areas

  • Mathematics (all)

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