Local Weyl modules for equivariant map algebras with free abelian group actions

Fourier, G., Khandai, T., Kus, D. and Savage, A. (2012) Local Weyl modules for equivariant map algebras with free abelian group actions. Journal of Algebra, 350(1), pp. 386-404. (doi: 10.1016/j.jalgebra.2011.10.018)

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Publisher's URL: http://dx.doi.org/10.1016/j.jalgebra.2011.10.018

Abstract

Suppose a finite group Γ acts on a scheme X and a finite-dimensional Lie algebra g. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from X to g. Examples include generalized current algebras and (twisted) multiloop algebras.<p></p> Local Weyl modules play an important role in the theory of finite-dimensional representations of loop algebras and quantum affine algebras. In the current paper, we extend the definition of local Weyl modules (previously defined only for generalized current algebras and twisted loop algebras) to the setting of equivariant map algebras where g is semisimple, X is affine of finite type, and the group Γ is abelian and acts freely on X. We do so by defining twisting and untwisting functors, which are isomorphisms between certain categories of representations of equivariant map algebras and their untwisted analogues. We also show that other properties of local Weyl modules (e.g. their characterization by homological properties and a tensor product property) extend to the more general setting considered in the current paper.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Fourier, Dr Ghislain
Authors: Fourier, G., Khandai, T., Kus, D., and Savage, A.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
Publisher:Elsevier
ISSN:0021-8693
ISSN (Online):1090-266X

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