The unipotent modules of GLn(Fq) via tableaux

Scott Andrews

The unipotent modules of GL_n(F_q) via tableaux

Scott Andrews

Mathematics Department

Research output: Contribution to conference › Paper › peer-review

Abstract

We construct the irreducible unipotent modules of the finite general linear groups from actions on tableaux. Our approach is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. We show that our modules are isomorphic to those previously constructed by James (1984), although the two presentations are quite different. Key to our construction are the generalized Gelfand-Graev representations of Kawanaka (1983).

Original language	English
State	Published - 2018
Event	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: 16 Jul 2018 → 20 Jul 2018

Conference

Conference	30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
Country/Territory	United States
City	Hanover
Period	16/07/18 → 20/07/18

Keywords

Finite general linear group
Generalized Gelfand-Graev representation
Tableaux
Unipotent representation

Cite this

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title = "The unipotent modules of GLn(Fq) via tableaux",

abstract = "We construct the irreducible unipotent modules of the finite general linear groups from actions on tableaux. Our approach is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. We show that our modules are isomorphic to those previously constructed by James (1984), although the two presentations are quite different. Key to our construction are the generalized Gelfand-Graev representations of Kawanaka (1983).",

keywords = "Finite general linear group, Generalized Gelfand-Graev representation, Tableaux, Unipotent representation",

author = "Scott Andrews",

note = "Publisher Copyright: {\textcopyright} FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 ; Conference date: 16-07-2018 Through 20-07-2018",

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AU - Andrews, Scott

PY - 2018

Y1 - 2018

N2 - We construct the irreducible unipotent modules of the finite general linear groups from actions on tableaux. Our approach is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. We show that our modules are isomorphic to those previously constructed by James (1984), although the two presentations are quite different. Key to our construction are the generalized Gelfand-Graev representations of Kawanaka (1983).

AB - We construct the irreducible unipotent modules of the finite general linear groups from actions on tableaux. Our approach is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction exists. We show that our modules are isomorphic to those previously constructed by James (1984), although the two presentations are quite different. Key to our construction are the generalized Gelfand-Graev representations of Kawanaka (1983).

KW - Finite general linear group

KW - Generalized Gelfand-Graev representation

KW - Tableaux

KW - Unipotent representation

UR - http://www.scopus.com/inward/record.url?scp=85089352066&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85089352066

T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

The unipotent modules of GL_n(F_q) via tableaux

Abstract

Conference

Keywords

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