Duke Mathematical Journal

Geometric realizations of Wakimoto modules at the critical level

Edward Frenkel and Dennis Gaitsgory

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Abstract

We study the Wakimoto modules over the affine Kac-Moody algebras at the critical level from the point of view of the equivalences of categories proposed in our previous works, relating categories of representations and certain categories of sheaves. In particular, we explicitly describe geometric realizations of Wakimoto modules as Hecke eigen-D-modules on the affine Grassmannian and as quasi-coherent sheaves on the flag variety of the Langlands dual group

Article information

Source
Duke Math. J., Volume 143, Number 1 (2008), 117-203.

Dates
First available in Project Euclid: 23 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1211574665

Digital Object Identifier
doi:10.1215/00127094-2008-017

Mathematical Reviews number (MathSciNet)
MR2414746

Zentralblatt MATH identifier
1215.17016

Subjects
Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Secondary: 81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]

Citation

Frenkel, Edward; Gaitsgory, Dennis. Geometric realizations of Wakimoto modules at the critical level. Duke Math. J. 143 (2008), no. 1, 117--203. doi:10.1215/00127094-2008-017. https://projecteuclid.org/euclid.dmj/1211574665


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