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arXiv · 2012.09893

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.

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BibTeXRIS

Nadya Gurevich, Edmund Karasiewicz. 2020-12-17. The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups. https://arxiv.org/abs/2012.09893

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