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

Author(s): Joseph Chuang; Hyohe Miyachi; Kai Meng Tan
Journal: Trans. Amer. Math. Soc. 360 (2008), 1179-1191.
MSC (2000): Primary 17B37; Secondary 20C08
Posted: October 2, 2007
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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: 10.1090/S0002-9947-07-04202-X
PII: S 0002-9947(07)04202-X
Received by editor(s): July 23, 2005
Posted: October 2, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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