Sign sequences and decomposition numbers

Tan, Kai; Teo, Wei Hao

doi:10.1090/S0002-9947-2013-05860-6

Sign sequences and decomposition numbers
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by Kai Meng Tan and Wei Hao Teo PDF

Trans. Amer. Math. Soc. 365 (2013), 6385-6401 Request permission

Abstract:

We obtain a closed formula for the $v$-decomposition numbers $d_{\lambda \mu }(v)$ arising from the canonical basis of the Fock space representation of $U_v(\widehat {\mathfrak {sl}}_e)$, where the partition $\lambda$ is obtained from $\mu$ by moving some nodes in its Young diagram, all of which have the same $e$-residue. We also show that when these $v$-decomposition numbers are evaluated at $v=1$, we obtain the corresponding decomposition numbers for the Schur algebras and symmetric groups.

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