The spherical Hecke algebra for affine Kac-Moody groups I

Alexander Braverman; David Kazhdan

doi:10.4007/annals.2011.174.3.5

The spherical Hecke algebra for affine Kac-Moody groups I

Alexander Braverman^*
, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalizationof the Satake isomorphism for this algebra, relating it to integrable repre-sentations of the Langlands dual affine Kac-Moody group. In the nextpublication we shall use these results to define and study the notion ofHecke eigenfunction for the group G_aff.

Original language	English
Pages (from-to)	1603-1642
Number of pages	40
Journal	Annals of Mathematics
Volume	174
Issue number	3
DOIs	https://doi.org/10.4007/annals.2011.174.3.5
State	Published - Nov 2011

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10.4007/annals.2011.174.3.5

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title = "The spherical Hecke algebra for affine Kac-Moody groups I",

abstract = "We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalizationof the Satake isomorphism for this algebra, relating it to integrable repre-sentations of the Langlands dual affine Kac-Moody group. In the nextpublication we shall use these results to define and study the notion ofHecke eigenfunction for the group Gaff.",

author = "Alexander Braverman and David Kazhdan",

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AB - We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalizationof the Satake isomorphism for this algebra, relating it to integrable repre-sentations of the Langlands dual affine Kac-Moody group. In the nextpublication we shall use these results to define and study the notion ofHecke eigenfunction for the group Gaff.

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The spherical Hecke algebra for affine Kac-Moody groups I

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