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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The combinatorics of Coxeter categories
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by Peter Fiebig PDF
Trans. Amer. Math. Soc. 360 (2008), 4211-4233 Request permission

Abstract:

We present an alternative construction of Soergel’s category of bimodules associated to a reflection faithful representation of a Coxeter system. We show that its objects can be viewed as sheaves on the associated moment graph. We introduce an exact structure and show that Soergel’s “special” bimodules are the projective objects. Then we construct the indecomposable projectives by both a global and a local method, discuss a version of the Kazhdan-Lusztig conjecture and prove it for universal Coxeter systems.
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Additional Information
  • Peter Fiebig
  • Affiliation: Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany
  • Received by editor(s): July 18, 2006
  • Published electronically: March 14, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 4211-4233
  • MSC (2000): Primary 20F55; Secondary 17B67
  • DOI: https://doi.org/10.1090/S0002-9947-08-04376-6
  • MathSciNet review: 2395170