Branching graphs for finite unitary groups in nondefining characteristic

We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of the crystal graph of well-chosen Fock spaces, under favorable conditions. Besides, we give the combinatorial formula to...

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Published in:Communications in algebra 2017-02, Vol.45 (2), p.561-574
Main Authors: Gerber, Thomas, Hiss, Gerhard
Format: Article
Language:English
Subjects:
Algebra
Branching graph
Combinatorial analysis
Crystal defects
crystal graph
Crystals
endomorphism algebra
Fock space
Graphs
Harish-Chandra series
Iwahori-Hecke algebra
Mathematical analysis
Modules
unitary group
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description We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of the crystal graph of well-chosen Fock spaces, under favorable conditions. Besides, we give the combinatorial formula to pass from one to the other in the case of modules arising from cuspidal modules of defect 0. This partly proves a recent conjecture of Jacon and the authors.
doi_str_mv 10.1080/00927872.2016.1175610
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subjects Algebra
Branching graph
Combinatorial analysis
Crystal defects
crystal graph
Crystals
endomorphism algebra
Fock space
Graphs
Harish-Chandra series
Iwahori-Hecke algebra
Mathematical analysis
Modules
unitary group
title Branching graphs for finite unitary groups in nondefining characteristic
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