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

Chuang, Joseph; Miyachi, Hyohe; Tan, Kai

doi:10.1090/S0002-9947-07-04202-X

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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