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Fusion and convolution: applications to affine Kac-Moody algebras at the critical level | | Edward Frenkel
; Dennis Gaitsgory
; | | Date: |
11 Nov 2005 | | Subject: | Representation Theory; Algebraic Geometry; Quantum Algebra | | Abstract: | Let g be a semi-simple Lie algebra, and let g^ be the corresponding affine Kac-Moody algebra. Consider the category of g^-modules at the critical level, on which the action of the Iwahori subalgebra integrates to algebraic action of the Iwahori subgroup I. We study the convolution functors on this category M --> Z(V) * M, where Z(V) is the "central" sheaf on the affine flag scheme G((t))/I, corresponding to a representation V of the Langlands dual group of G (see [Ga]).
We show that each object M of our category is an "eigen-module" with respect to these functors, that is Z(V) * M is isomorphic to V otimes_{Z} M, where V is a vector bundle, corresponding to V, defined over the spectrum of the center Z of our category.
In order to establish this isomorphism, we interpret the two sides functorially, using the notion of fusion product of modules over the affine Kac-Moody algebra. | | Source: | arXiv, math/0511284 | | Services: | Article forum | Review this article | Full Text PDF | Add to favorites | 
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