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Rim hook tableaux and Kostant’s \(\eta\)-function coefficients. (English) Zbl 1056.05144
Summary: 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.

MSC:
05E10 Combinatorial aspects of representation theory
05E05 Symmetric functions and generalizations
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