Elliptic central characters and blocks of finite dimensional representations of quantum affine algebras

Etingof, Pavel; Moura, Adriano

doi:10.1090/S1088-4165-03-00201-2

Elliptic central characters and blocks of finite dimensional representations of quantum affine algebras
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by Pavel I. Etingof and Adriano A. Moura

Represent. Theory 7 (2003), 346-373

DOI: https://doi.org/10.1090/S1088-4165-03-00201-2

Published electronically: August 26, 2003

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Abstract:

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

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