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Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution
- Source :
- SIGMA 14 (2018), 007, 18 pages
- Publication Year :
- 2017
-
Abstract
- We study the effect of Alvis-Curtis duality on the unipotent representations of $\mathrm{GL}_n(q)$ 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 $q$ modulo $\ell$.
- Subjects :
- Mathematics - Representation Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- SIGMA 14 (2018), 007, 18 pages
- Publication Type :
- Report
- Accession number :
- edsarx.1706.04743
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3842/SIGMA.2018.007