Thomas Gerber, Gerhard Hiss
Published 2015-02-06Version 1
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 favourable 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.
Harish-Chandra series in finite unitary groups and crystal graphs
On Harish-Chandra series of finite unitary groups and the $\mathfrak{sl}_\infty$-crystal on level $2$ Fock spaces
Weight 2 blocks of general linear groups and modular Alvis-Curtis duality
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