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Rim Hook Tableaux and Kostant's $\eta$-Function Coefficients

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arxiv math/0201003 v3 pith:SF354H4C submitted 2001-12-31 math.CO math.RT

Ron M. Adin , Avital Frumkin This is my paper · ORCID
classification math.COmath.RT
keywords coefficientsformulafunctionhookkostanttableauxapplicationarbitrary
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abstract

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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 7 citations worldwide. Full citation record

  1. On Hecke and asymptotic categories for a family of complex reflection groups

    math.RT 2024-09 unverdicted novelty 6.0 of 10

    Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.

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