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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Geometry of the Jantzen region in Lusztig’s conjecture
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by Brian D. Boe PDF
Math. Comp. 70 (2001), 1265-1280 Request permission

Abstract:

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
  • Email: brian@math.uga.edu
  • Received by editor(s): May 22, 1998
  • Received by editor(s) in revised form: July 6, 1999
  • Published electronically: March 14, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 1265-1280
  • MSC (2000): Primary 20G05; Secondary 20F55, 51F15
  • DOI: https://doi.org/10.1090/S0025-5718-00-01220-5
  • MathSciNet review: 1709146