Level zero integrable modules with finite-dimensional weight spaces for the graded Lie tori

Abstract: An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite-dimensional weight spaces. The centres of both affine and toroidal Lie algebras are spanned by finitely many elements. If all these central elements act trivially on a module, we say that the representation has level zero, otherwise it is said to have non-zero level. The classification of these irreducible integrable modules with finite-dimensional weight spaces over the affine Kac-Moody algebras (both twisted and untwisted) have been completely settled by V. Chari and A. Pressley. This was subsequently generalized by S. Eswara Rao for the (untwisted) toroidal Lie algebras. Recently, the aforementioned irreducible integrable modules of non-zero level have been classified for a more general class of Lie algebras, namely the graded Lie tori, which are multivariable generalizations of twisted affine Kac-Moody algebras. In this talk, I shall address the mutually exclusive problem and henceforth classify all the level zero irreducible integrable modules with finite-dimensional weight spaces for this graded Lie tori.

combinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

ARCSIN - Algebra, Representations, Combinatorics and Symmetric functions in INdia

Series comments: Timings may vary depending on the time zone of the speakers.