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

Nadya Gurevich, Edmund Karasiewicz

Research output: Working paper/PreprintPreprint

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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
StatePublished - 2020

Publication series

NameArxiv preprint

Keywords

  • Mathematics - Representation Theory
  • Mathematics - Number Theory

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