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

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

2002-04-24

arxiv.org/abs/math/0204302v1

Mathematics

Quantum Algebra

28 pages

Scientific paper

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.

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