publication . Part of book or chapter of book . Preprint . 2014

inverse satake transforms

Sakellaridis, Yiannis;
Open Access
  • Published: 08 Oct 2014
  • Publisher: Springer International Publishing
Abstract
Let H be a split reductive group over a local non-archimedean field, and let 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.
Subjects
arXiv: Mathematics::Representation TheoryMathematics::Number Theory
free text keywords: Reductive group, Inverse, Pure mathematics, Dual group, Mathematics, Generating function, Hecke algebra, Langlands dual group, Mathematics - Representation Theory, Mathematics - Number Theory
Funded by
NSF| Spherical varieties in the Langlands program
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1101471
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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publication . Part of book or chapter of book . Preprint . 2014

inverse satake transforms

Sakellaridis, Yiannis;