2011/03/31 by Ghislain Fourier, Tanusree Khandai, Deniz Kus +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #math.RA #math.RT #msc:17B10 #msc:17B65
paper · pdf · doi:10.1016/j.jalgebra.2011.10.018
published as J. Algebra 350 (2012), 386--404 · 18 pages. v2: Minor corrections
openalex publication_date 2011/10/28 · arxiv created 2011/11/02 · arxiv updated 2012/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose a finite group 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. 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 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.