Thomas Gerber, Gerhard Hiss, Nicolas Jacon
Published 2014-08-06Version 1
The distribution of the unipotent modules (in non-defining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph of an integrable module for a certain quantum group. Evidence for our conjectures is presented, as well as proofs for some of their consequences for the crystal graphs involved. In the course of our work we also generalize Harish-Chandra theory for some of the finite classical groups, and we introduce their Harish-Chandra branching graphs.
On Harish-Chandra series of finite unitary groups and the $\mathfrak{sl}_\infty$-crystal on level $2$ Fock spaces
Branching graphs for finite unitary groups in non-defining characteristic
Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
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