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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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Geometric braid group action on derived categories of coherent sheaves
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by Simon Riche; \\ with a joint appendix with Roman Bezrukavnikov PDF
Represent. Theory 12 (2008), 131-169 Request permission


In this paper we give, for semi-simple groups without factors of type $\mathbf {G}_2$, a geometric construction of a braid group action on $\mathcal {D}^b \operatorname {Coh}(\widetilde {\mathfrak {g}})$ extending the action constructed by Bezrukavnikov, Mirković and Rumynin in the context of localization in positive characteristic. It follows that this action extends to characteristic zero, where it also has some nice representation-theoretic interpretations. The argument uses a presentation of the affine braid group analogous to the “Bernstein presentation” of the corresponding Hecke algebra (this presentation was suggested by Lusztig; it is worked out in the appendix, written jointly with Roman Bezrukavnikov).
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Additional Information
  • Simon Riche
  • Affiliation: Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu (UMR 7586 du CNRS), Équipe d’Analyse Algébrique, 175, rue du Chevaleret, 75013 Paris, France
  • MR Author ID: 834430
  • Email:
  • Roman Bezrukavnikov
  • Affiliation: Massachusetts Institute of Technology, Cambridge, Massachusetts
  • MR Author ID: 347192
  • Email:
  • Received by editor(s): March 12, 2007
  • Received by editor(s) in revised form: July 23, 2007
  • Published electronically: March 10, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 12 (2008), 131-169
  • MSC (2000): Primary 14M15; Secondary 20F55, 18E30
  • DOI:
  • MathSciNet review: 2390670