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

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Fiebig P
Zeitschrift: Journal of the American Mathematical Society
Verlag: American Mathematical Society
Jahr der Veröffentlichung: 2011
Band: 24
Heftnummer: 1
Seitenbereich: 133-181
ISSN: 0894-0347


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.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Fiebig, Peter Prof. Dr.
Professur für Mathematik (Algebra und Geometrie)


Zitierweisen

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.

BibTeX: 

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