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Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian

Zhu, Xinwen (2009) Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian. Advances in Mathematics, 221 (2). pp. 570-600. ISSN 0001-8708.

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Let G be a simple algebraic group defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T-fixed point subscheme [formula] of the Schubert variety [formula] in the affine Grassmannian GrG is a finite scheme. We prove that for all such λ if G is of type A or D and for many of them if G is of type E, there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (twisted by certain line bundle on GrG) of [formula]. We use this fact to give a geometrical proof of the Frenkel–Kac–Segal isomorphism between basic representations of affine algebras of A, D, E type and lattice vertex algebras.

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Additional Information:Copyright © 2009 Elsevier. Received 18 November 2008; accepted 13 January 2009. Communicated by Roman Bezrukavnikov . The author is very grateful to his advisor, Edward Frenkel, for many stimulating discussions and careful reading of the early draft. Without his encouragement, this paper would have never been written up. The author is also grateful to Joel Kamnitzer and Zhiwei Yun for very useful discussions, and especially to the referee for a meticulous review which has greatly improved the exposition.
Subject Keywords:Basic representation; Frenkel–Kac–Segal isomorphism; Affine Grassmannian
Issue or Number:2
Record Number:CaltechAUTHORS:20140919-152325484
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49874
Deposited By: George Porter
Deposited On:23 Sep 2014 03:57
Last Modified:03 Oct 2019 07:18

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