Rim hook tableaux and Kostant's η-function coefficients

Ron M. Adin, Avital Frumkin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 η-function, avoiding most of the original machinery.

Original languageEnglish
Pages (from-to)492-511
Number of pages20
JournalAdvances in Applied Mathematics
Volume33
Issue number3
DOIs
StatePublished - Oct 2004

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: radin@math.biu.ac.il (R.M. Adin), frumkin@math.tau.ac.il (A. Frumkin). 1 Research supported in part by the Israel Science Foundation, founded by the Israel Academy of Sciences and Humanities, and by an internal research grant from Bar-Ilan University.

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