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Kleshchev's decomposition numbers and branching coefficients in the Fock space


Authors: Joseph Chuang, Hyohe Miyachi and Kai Meng Tan
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
Published electronically: October 2, 2007
MathSciNet review: 2357693
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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
Email: miyachi@math.nagoya-u.ac.jp

Kai Meng Tan
Affiliation: Department of Mathematics, National University of Singapore, 2, Science Drive 2, Singapore 117543
Email: tankm@nus.edu.sg

DOI: https://doi.org/10.1090/S0002-9947-07-04202-X
Received by editor(s): July 23, 2005
Published electronically: October 2, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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