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arXiv math/02010032002-01math.COmath.RT

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

Ron M. Adin, Avital Frumkin

备注：: 24 pages; minor changes, more detailed introduction

英文摘要：

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 $η$-function, avoiding most of the original machinery.

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