Green polynomials at roots of unity and Springer modules for the symmetric groups |
| |
Authors: | Hideaki Morita |
| |
Affiliation: | Department of Mathematics, Oyama National College of Technology, Oyama 323-0806, Japan |
| |
Abstract: | We consider the Green polynomials at roots of unity. We obtain a recursive formula for the Green polynomials at roots of unity whose orders do not exceed some positive integer. The formula is described in a combinatorial manner. The coefficients of the recursive formula are realized by the cardinality of a set of permutations. The formula gives an interpretation of a combinatorial property on a family of graded modules for the symmetric group in terms of representation theory. |
| |
Keywords: | Symmetric groups Symmetric functions Springer modules Green polynomials Roots of unity Permutation enumeration |
本文献已被 ScienceDirect 等数据库收录! |