Elliptic Central Characters and Blocks of Finite Dimensional Representations of Quantum Affine Algebras

Abstract

The category of finite dimensional (type 1) representations of a quantum affine algebra $U_q(\hat{\mathfrak{g}})$ is not semisimple. However, as any abelian category with finite-length objects, it admits a unique decomposition into a direct sum of indecomposable subcategorie (blocks). We define the elliptic central character of a finite dimensional (type 1) representation of $U_q(\hat{\mathfrak{g}})$. Then we show that the block decomposition of this category is paramentrized by these elliptic central characters.

28 pages

References in corpus (3)

• Deformations of W-algebras associated to simple Lie algebras
• Braid Group Actions and Tensor Products
• Elliptic Dynamical R-Matrices from the Monodromy of the q-Knizhnik-Zamolodchikov Equations for the Standard Representation of Uq(sl(n+1))

Cited by in corpus (1)

• Universal K-matrices for quantum Kac-Moody algebras