Rim Hook Tableaux and Kostant's $η$-Function Coefficients

Details Rim Hook Tableaux and Kostant's $η$-Function Coefficients Rim Hook Tableaux and Kostant's $η$-Function Coefficients

2001-12-31

arxiv.org/abs/math/0201003v3

Mathematics

Combinatorics

24 pages; minor changes, more detailed introduction

Scientific paper

Using a 0/1 encoding of Young diagrams and its consequences for rim hook tableaux, we prove a reduction formula of Littlewood for arbitrary characters of the symmetric group, evaluated at elements with all cycle lengths divisible by a given integer. As an application, we find explicitly the coefficients in a formula of Kostant for certain powers of the Dedekind $\eta$-function, avoiding most of the original machinery.

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