Branching graphs for finite unitary groups in nondefining characteristic. Issue 2 (1st February 2017)

• Record Type: Journal Article
• Authors: Gerber, Thomas; Hiss, Gerhard
• Is Part Of: Communications in algebra. Volume 45:Issue 2(2017)
• Page Start: 561
• Page End: 574
• Publication Date: 2017-02-01
• Subjects: Branching graph -- crystal graph -- endomorphism algebra -- Fock space -- Harish-Chandra series -- Iwahori-Hecke algebra -- unitary group; 20C33 -- 20C08 -- 20G42 -- 17B37; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1175610
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: 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.