Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Dudas, O., Jacon, N.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209457
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution / O. Dudas , N. Jacon // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ.

We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q) in non-defining characteristic ℓ. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves b...