Representations of affine Kac-Moody groups over local and global fields: a survey of some recent results
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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.Keywords
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This publication has 20 references indexed in Scilit:
- Pursuing the double affine Grassmannian II: ConvolutionAdvances in Mathematics, 2012
- Affine Gindikin–Karpelevich Formula via Uhlenbeck SpacesSpringer Proceedings in Mathematics, 2011
- On the Siegel-Weil theorem for loop groups, IDuke Mathematical Journal, 2011
- Pursuing the double affine Grassmannian, I: Transversal slices via instantons on Ak-singularitiesDuke Mathematical Journal, 2010
- Theta functions and Weil representations of loop symplectic groupsDuke Mathematical Journal, 2008
- Representations of algebraic groups over a 2-dimensional local fieldGeometric and Functional Analysis, 2004
- Double affine Hecke algebras and 2-dimensional local fieldsJournal of the American Mathematical Society, 2000
- The Lefschetz trace formula for algebraic stacksInventiones Mathematicae, 1993
- The Yang-Mills equations over Riemann surfacesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1983
- Spherical functions on a 𝔭-adic Chevalley groupBulletin of the American Mathematical Society, 1968