Inverse Satake Transforms

  • Yiannis SakellaridisEmail author
Conference paper
Part of the Simons Symposia book series (SISY)


Let H be a split reductive group over a local non-Archimedean field, and let \(\check {H}\) denote its Langlands dual group. We present an explicit formula for the generating function of an unramified L-function associated to a highest weight representation of the dual group, considered as a series of elements in the Hecke algebra of H. This offers an alternative approach to a solution of the same problem by Wen-Wei Li. Moreover, we generalize the notion of “Satake transform” and perform the analogous calculation for a large class of spherical varieties.


Satake transform Spherical varieties Spherical functions L-functions 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics & Computer ScienceRutgers University - NewarkNewarkUSA

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