Abstract
We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for this algebra, relating it to integrable representations of the Langlands dual affine Kac-Moody group. In the next publication we shall use these results to define and study the notion of Hecke eigenfunction for the group $G_{\rm aff}$.
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[bf]
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@article {bf, MRKEY = {2656088},
AUTHOR = {Braverman, Alexander and Finkelberg, Michael},
TITLE = {Pursuing the double affine {G}rassmannian. {I}. {T}ransversal slices via instantons on {$A\sb k$}-singularities},
JOURNAL = {Duke Math. J.},
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VOLUME = {152},
YEAR = {2010},
NUMBER = {2},
PAGES = {175--206},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {14D24 (14D21 14F43 14J60 20G44)},
MRNUMBER = {2656088},
DOI = {10.1215/00127094-2010-011},
ZBLNUMBER={1200.14083},
} -
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@misc{bf1,
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} -
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NOTE={in preparation},
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