English

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

Representation Theory 2018-01-31 v3

Abstract

We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q)\mathrm{GL}_n(q) in non-defining characteristic \ell. 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 both \ell and the order of qq modulo \ell.

Cite

@article{arxiv.1706.04743,
  title  = {Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution},
  author = {Olivier Dudas and Nicolas Jacon},
  journal= {arXiv preprint arXiv:1706.04743},
  year   = {2018}
}
R2 v1 2026-06-22T20:19:24.464Z