Sheaves on affine Schubert varieties, modular representations, and Lusztig's conjecture

Fiebig P (2011)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2011

Journal

Publisher: American Mathematical Society

Book Volume: 24

Pages Range: 133-181

Journal Issue: 1

DOI: 10.1090/S0894-0347-2010-00679-0

Abstract

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 ch k>0) or to modules over the small quantum group (for ch 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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How to cite

APA:

Fiebig, P. (2011). Sheaves on affine Schubert varieties, modular representations, and Lusztig's conjecture. Journal of the American Mathematical Society, 24(1), 133-181. https://dx.doi.org/10.1090/S0894-0347-2010-00679-0

MLA:

Fiebig, Peter. "Sheaves on affine Schubert varieties, modular representations, and Lusztig's conjecture." Journal of the American Mathematical Society 24.1 (2011): 133-181.

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