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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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Existence of Kirillov鈥揜eshetikhin crystals for nonexceptional types
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by Masato Okado and Anne Schilling PDF
Represent. Theory 12 (2008), 186-207 Request permission

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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Additional 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