Green polynomials at roots of unity and Springer modules for the symmetric groups

• Autores: Hideaki Morita
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 1, 2007, págs. 277-292
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.10.008
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• Resumen

  • 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.