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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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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 PDF
Represent. Theory 7 (2003), 346-373 Request permission


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
  • MR Author ID: 289118
  • Email:
  • Adriano A. Moura
  • Affiliation: IMECC/UNICAMP, Caixa Postal: 6065, CEP: 13083-970, Campinas SP Brazil
  • Email:
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 346-373
  • MSC (2000): Primary 20G42
  • DOI:
  • MathSciNet review: 2017062