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

Authors: Pavel I. Etingof and Adriano A. Moura
Journal: Represent. Theory 7 (2003), 346-373
MSC (2000): Primary 20G42
Published electronically: August 26, 2003
MathSciNet review: 2017062
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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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Additional Information

Pavel I. Etingof
Affiliation: Massachussets Institute of Technology, 77 Massachussets Ave., Room 2-176, Cambridge, Massachusetts 02139

Adriano A. Moura
Affiliation: IMECC/UNICAMP, Caixa Postal: 6065, CEP: 13083-970, Campinas SP Brazil

Received by editor(s): April 24, 2002
Received by editor(s) in revised form: December 10, 2002
Published electronically: August 26, 2003
Dedicated: For Igor Frenkel, on the occasion of his 50th birthday
Article copyright: © Copyright 2003 American Mathematical Society

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