Weyl modules for multiloop algebras
Ghislain Fourier, Tanusree Khandai, Deniz Kus
TL;DR
This paper extends the definition of Weyl modules to twisted multiloop algebras and establishes an identification with modules for untwisted multiloop algebras, advancing the understanding of their representation theory.
Contribution
It provides a categorical definition for Weyl modules in the twisted case and links their modules to those of untwisted multiloop algebras.
Findings
Categorical definition of Weyl modules for twisted multiloop algebras
Identification of finite-dimensional modules between twisted and untwisted cases
Extension of homological properties to the twisted setting
Abstract
Global and local Weyl modules for the untwisted multiloop Lie algebras were defined by Chari, the first and the second author via homological properties. In this paper we extended the ideas to give a categorical definition of the Weyl modules for twisted multiloop algebras. Our methods led us to describe an identification of the finite--dimensional highest weight modules for twisted multiloop algebras with suitably chosen finite--dimensional highest weight modules for untwisted multiloop algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry