Geometric realizations of affine Kac-Moody algebras
Vyacheslav Futorny, Libor K\v{r}i\v{z}ka, Petr Somberg
TL;DR
This paper develops new geometric methods to construct free field realizations of affine Kac-Moody algebras, expanding the understanding of their representations through explicit module constructions related to flag manifolds.
Contribution
It introduces a broad class of irreducible modules for affine Kac-Moody algebras, generalizing previous special cases via geometric representation theory.
Findings
Explicit construction of irreducible modules for affine Kac-Moody algebras.
New free field realizations motivated by geometric representation theory.
Coverage of all known special cases through a unified approach.
Abstract
The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an explicit construction of a large class of irreducible modules associated with certain parabolic subalgebras covering all known special cases.
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