Differential operators and the loop group via chiral algebras

2000/09/01 by Sergey Arkhipov, S. Arkhipov, Arkhipov, S. +3
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0009007

Revised version, Section 6 added

openalex publication_date 2000/09/01 · arxiv created 2001/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be an algebraic group and let \widetilde\mathfrak g be the corresponding affine algebra on some level. Consider the induced module V:=Ind^\widetilde\mathfrak g_\mathfrak g[[t]](O_G[[t]]), where O_G[[t]] is the ring of regular functions on the group G[[t]]. In this paper we show that V is naturally a vertex operator algebra, which is "responsible" for D-modules on the loop group G((t)). Using the techiques of VOA we show that V is in fact a bimodule over the affine algebra. In addition, we show that V possesses a remarkable property related to its BRST reduction with respect to \widetilde\mathfrak g. This paper has a considerable intersection with a recent preprint of Gorbunov, Malikov and Schechtman.

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