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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Sheaves on affine Schubert varieties, modular representations, and Lusztig’s conjecture
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by Peter Fiebig PDF
J. Amer. Math. Soc. 24 (2011), 133-181 Request permission


We relate a certain category of sheaves of $k$-vector spaces on a complex affine Schubert variety to modules over the $k$-Lie algebra (for $\operatorname {char} k>0$) or to modules over the small quantum group (for $\operatorname {char} k=0$) associated to the Langlands dual root datum. As an application we give a new proof of Lusztig’s conjecture on quantum characters and on modular characters for almost all characteristics. Moreover, we relate the geometric and representation-theoretic sides to sheaves on the underlying moment graph, which allows us to extend the known instances of Lusztig’s modular conjecture in two directions: We give an upper bound on the exceptional characteristics and verify its multiplicity-one case for all relevant primes.
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Additional Information
  • Peter Fiebig
  • Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, Bismarckstr. $1\frac {1}{2}$, 91054 Erlangen, Germany
  • Email:
  • Received by editor(s): June 24, 2008
  • Received by editor(s) in revised form: November 26, 2009, and July 16, 2010
  • Published electronically: September 23, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 133-181
  • MSC (2010): Primary 20C20; Secondary 55N30
  • DOI:
  • MathSciNet review: 2726602