TY - JOUR
T1 - Rim hook tableaux and Kostant's η-function coefficients
AU - Adin, Ron M.
AU - Frumkin, Avital
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (R.M. Adin), [email protected] (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.
PY - 2004/10
Y1 - 2004/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=4344605501&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2003.06.004
DO - 10.1016/j.aam.2003.06.004
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AN - SCOPUS:4344605501
SN - 0196-8858
VL - 33
SP - 492
EP - 511
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
IS - 3
ER -