Geodesic
The Unipotent Modules of GLn(Fq) via Tableaux
Séminaire lotharingien de combinatoire, 80B (2018)

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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). 

@article{SLC_2018_80B_a23,
     author = {Scott Andrews},
     title = {The {Unipotent} {Modules} of {GLn(Fq)} via {Tableaux}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a23/}
}
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AU  - Scott Andrews
TI  - The Unipotent Modules of GLn(Fq) via Tableaux
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a23/
ID  - SLC_2018_80B_a23
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%0 Journal Article
%A Scott Andrews
%T The Unipotent Modules of GLn(Fq) via Tableaux
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a23/
%F SLC_2018_80B_a23
Scott Andrews. The Unipotent Modules of GLn(Fq) via Tableaux. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a23/