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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Projective rational smoothness of varieties of representations for quivers of type $A$
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by Ralf Schiffler PDF
Represent. Theory 7 (2003), 549-586 Request permission


Let ${\mathbf U}^+$ be the positive part of the quantized enveloping algebra ${\mathbf U}$ of type $A_n$. The change of basis between canonical, and PBW-basis of ${\mathbf U}^+$ has a geometric interpretation in terms of local intersection cohomology of some affine algebraic varieties, namely the Zariski closures of orbits of representations of a quiver of type $A_n$. In this paper we study the local rational smoothness of these orbit closures and, in particular, the rational smoothness of their projectivization.
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Additional Information
  • Ralf Schiffler
  • Affiliation: Département de mathématiques, Université du Québec à Montréal, case postale 8888, succursale Centre-Ville, Montréal (Québec), H3C 3P8 Canada
  • MR Author ID: 724459
  • Email:
  • Received by editor(s): October 24, 2002
  • Received by editor(s) in revised form: September 2, 2003
  • Published electronically: November 18, 2003
  • Additional Notes: The author was supported in part by FCAR Grant
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 549-586
  • MSC (2000): Primary 17B37; Secondary 32S60, 16G70
  • DOI:
  • MathSciNet review: 2017067