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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2024 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

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.
References
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Bibliographic Information
  • Pavel I. Etingof
  • Affiliation: Massachussets Institute of Technology, 77 Massachussets Ave., Room 2-176, Cambridge, Massachusetts 02139
  • MR Author ID: 289118
  • Email: etingof@math.mit.edu
  • Adriano A. Moura
  • Affiliation: IMECC/UNICAMP, Caixa Postal: 6065, CEP: 13083-970, Campinas SP Brazil
  • Email: adrianoam@ime.unicamp.br
  • 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: https://doi.org/10.1090/S1088-4165-03-00201-2
  • MathSciNet review: 2017062