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

Published 17 Dec 2020 in math.RT and math.NT | (2012.09893v1)

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.

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