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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 007, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.007 (Mi sigma1306) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

Olivier Dudasa, Nicolas Jaconb

a Université Paris Diderot, UFR de Mathématiques, Bâtiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris CEDEX 13, France
b Université de Reims Champagne-Ardenne, UFR Sciences exactes et naturelles, Laboratoire de Mathématiques EA 4535, Moulin de la Housse BP 1039, 51100 Reims, France
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DOI: https://doi.org/10.3842/SIGMA.2018.007
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 $\ell$.
Keywords: Mullineux involution; Alvis–Curtis duality; crystal graph; Harish-Chandra theory.
Funding agency Grant number
Agence Nationale de la Recherche ANR-16-CE40-0010-01
The authors gratefully acknowledge financial support by the ANR grant GeRepMod ANR-16-CE40-0010-01.
Received: June 17, 2017; in final form January 22, 2018; Published online January 30, 2018
Bibliographic databases:
Document Type: Article
MSC: 20C20; 20C30; 05E10
Language: English
Citation: Olivier Dudas, Nicolas Jacon, “Alvis–Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution”, SIGMA, 14 (2018), 007, 18 pp.
Citation in format AMSBIB
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\by Olivier~Dudas, Nicolas~Jacon
\paper Alvis--Curtis Duality for Finite General Linear Groups and a~Generalized Mullineux Involution
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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