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Geometry of the Jantzen region in Lusztig's conjecture

Author: Brian D. Boe
Journal: Math. Comp. 70 (2001), 1265-1280
MSC (2000): Primary 20G05; Secondary 20F55, 51F15
Published electronically: March 14, 2000
MathSciNet review: 1709146
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Abstract | References | Similar Articles | Additional Information


The Lusztig Conjecture expresses the character of a finite-dimensional irreducible representation of a reductive algebraic group $G$ in prime characteristic as a linear combination of characters of Weyl modules for $G$. The representations described by the conjecture are in one-to-one correspondence with the (finitely many) alcoves in the intersection of the dominant cone and the so-called Jantzen region. Each alcove has a length, defined to be the number of alcove walls (hyperplanes) separating it from the fundamental alcove (the unique alcove in the dominant cone whose closure contains the origin). This article determines the maximum length of an alcove in the intersection of the dominant cone with the Jantzen region.

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Additional Information

Brian D. Boe
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403

Received by editor(s): May 22, 1998
Received by editor(s) in revised form: July 6, 1999
Published electronically: March 14, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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