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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 2020 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.


Existence of Kirillov鈥揜eshetikhin crystals for nonexceptional types
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by Masato Okado and Anne Schilling
Represent. Theory 12 (2008), 186-207
Published electronically: April 14, 2008

Erratum: Represent. Theory 12 (2008), 499-500.


Using the methods of Kang et al. and recent results on the characters of Kirillov鈥揜eshetikhin modules by Nakajima and Hernandez, the existence of Kirillov鈥揜eshetikhin crystals $B^{r,s}$ is established for all nonexceptional affine types. We also prove that the crystals $B^{r,s}$ of type $B_n^{(1)}$, $D_n^{(1)}$, and $A_{2n-1}^{(2)}$ are isomorphic to recently constructed combinatorial crystals for $r$ not a spin node.
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Bibliographic Information
  • Masato Okado
  • Affiliation: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
  • Email:
  • Anne Schilling
  • Affiliation: Department of Mathematics, University of California, One Shields Avenue, Davis, California 95616-8633
  • MR Author ID: 352840
  • ORCID: 0000-0002-2601-7340
  • Email:
  • Received by editor(s): August 8, 2007
  • Received by editor(s) in revised form: February 26, 2008
  • Published electronically: April 14, 2008

  • Dedicated: Dedicated to Professor Masaki Kashiwara on his sixtieth birthday
  • © Copyright 2008 American Mathematical Society
  • Journal: Represent. Theory 12 (2008), 186-207
  • MSC (2000): Primary 17B37, 81R50; Secondary 05E15, 81R10
  • DOI:
  • MathSciNet review: 2403558