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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* Corresponding author. E-mail addresses: email@example.com (R.M. Adin), firstname.lastname@example.org (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.