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Iwahori-Hecke algebras for $$p$$-adic loop groups. (English) Zbl 1345.22011
The paper under review develops the theory of the Iwahori-Hecke algebra associated to an untwisted affine Kac-Moody group over a non-archimedian local field. It is shown that this algebra is related to Cherednik’s double affine Hecke algebra. The authors also give an explicit description of the affine Satake isomorphism which generalizes Macdonald’s formula for spherical functions in the finite-dimensional case.

##### MSC:
 22E67 Loop groups and related constructions, group-theoretic treatment 20G44 Kac-Moody groups 20C08 Hecke algebras and their representations 11S85 Other nonanalytic theory
##### MathOverflow Questions:
Langlands correspondence for higher local fields?
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##### References:
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