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Green Polynomials and Hall-Littlewood Functions at Roots of Unity

✍ Scribed by Alain Lascoux; Bernard Leclerc; Jean-Yves Thibon

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 223 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1019

No coin nor oath required. For personal study only.

✦ Synopsis

We give some applications of our recent work [10] about Hall-Littlewood functions at roots of unity. In particular, we prove the two conjectures of N. Sultana [17] on specializations of Green polynomials, and we generalize classical results concerning characters of the symmetric group induced by maximal cyclic subgroups. We also give some new congruences for Kostka-Foulkes polynomials modulo cyclotomic polynomials.

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