Harish-Chandra Series in Finite Unitary Groups and Crystal Graphs

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. Eviden...

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Bibliographic Details
Published in:International mathematics research notices 2015-01
Main Authors: Gerber, T., Hiss, G., Jacon, N.
Format: Article
Language:English
Subjects:
Mathematics
Representation Theory
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Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnv058