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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Kleshchev’s decomposition numbers and branching coefficients in the Fock space
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by Joseph Chuang, Hyohe Miyachi and Kai Meng Tan PDF
Trans. Amer. Math. Soc. 360 (2008), 1179-1191 Request permission

Abstract:

We give combinatorial descriptions of some coefficients of the canonical basis of the $q$-deformed Fock space representation of $U_q(\widehat {\mathfrak {sl}}_e)$ and of some matrix entries for the action of the Chevalley generators $f_r$ with respect to the canonical basis. These are $q$-analogues of results of Kleshchev on decomposition numbers and branching coefficients for symmetric groups and Schur algebras.
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Additional Information
  • Joseph Chuang
  • Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
  • Email: joseph.chuang@bris.ac.uk
  • Hyohe Miyachi
  • Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
  • MR Author ID: 649846
  • Email: miyachi@math.nagoya-u.ac.jp
  • Kai Meng Tan
  • Affiliation: Department of Mathematics, National University of Singapore, 2, Science Drive 2, Singapore 117543
  • MR Author ID: 656415
  • Email: tankm@nus.edu.sg
  • Received by editor(s): July 23, 2005
  • Published electronically: October 2, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1179-1191
  • MSC (2000): Primary 17B37; Secondary 20C08
  • DOI: https://doi.org/10.1090/S0002-9947-07-04202-X
  • MathSciNet review: 2357693