Representations of affine Kac-Moody groups over local and global fields: a survey of some recent results

2012/05/04 by Braverman, Alexander, Kazhdan, David
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1205.0870

Abstract

Let G be a reductive algebraic group over a local field K or a global field F. It is well know that there exists a non-trivial and interesting representation theory of the group G(K) as well as the theory of automorphic forms on the corresponding adelic group. The purpose of this paper is to give a survey of some recent constructions and results, which show that there should exist an analog of the above theories in the case when G is replaced by the corresponding affine Kac-Moody group (which is essentially built from the formal loop group G((t)) of G). Specifically we discuss the following topics : affine (classical and geometric) Satake isomorphism, affine Iwahori-Hecke algebra, affine Eisenstein series and Tamagawa measure.

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