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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the spanning vectors of Lusztig cones
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by Robert Bédard
Represent. Theory 4 (2000), 306-329
Published electronically: July 31, 2000


For each reduced expression ${\mathbf i}$ of the longest element $w_0$ of the Weyl group $W$ of a Dynkin diagram $\Delta$ of type $A$, $D$ or $E$, Lusztig defined a cone ${\mathcal C}_{\mathbf i}$ such that there corresponds a monomial in the quantized enveloping algebra ${\mathbf U}$ of $\Delta$ to each element of ${\mathcal C}_{\mathbf i}$ and he asked under what circumstances these monomials belong to the canonical basis of ${\mathbf U}$. In this paper, we consider the case where ${\mathbf i}$ is a reduced expression adapted to a quiver $\Omega$ whose graph is $\Delta$ and we describe ${\mathcal C}_{\mathbf i}$ as the set of non-negative integral combination of spanning vectors. These spanning vectors are themselves described by using the Auslander-Reiten quiver of $\Omega$ and homological algebra.
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Bibliographic Information
  • Robert Bédard
  • Affiliation: Département de Mathématiques, Université du Québec à Montréal, C.P. 8888, Succ. Centre-Ville, Montréal, Québec, H3C 3P8, Canada
  • Email:
  • Received by editor(s): December 2, 1999
  • Received by editor(s) in revised form: May 27, 2000
  • Published electronically: July 31, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 306-329
  • MSC (2000): Primary 16G20, 16G70, 17B37
  • DOI:
  • MathSciNet review: 1773864