Spectral Characters of Finite-Dimensional Representations of Affine Algebras

Abstract

We introduce the notion of a spectral character for finite-dimensional representations of affine algebras. These can be viewed as a suitable q=1 limit of the elliptic characters defined by Etingof and Moura for quantum affine algebras. We show that these characters determine blocks of the category of finite-dimensional modules for affine algebras. To do this we use the Weyl modules defined by Chari and Pressley and some indecomposable reducible quotient of the Weyl modules.

More concise proofs for Propositions 1.2 and 2.4 added. To appear in Journal of Algebra