The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups

Nadya Gurevich, Edmund Karasiewicz

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Abstract

We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.

Original languageEnglish
Pages (from-to)11148-11179
Number of pages32
JournalInternational Mathematics Research Notices
Volume2022
Issue number14
DOIs
StatePublished - Jul 2021

Keywords

  • Mathematics - Representation Theory
  • Mathematics - Number Theory

ASJC Scopus subject areas

  • Mathematics (all)

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