Lusztig's conjecture as a moment graph problem

Beitrag in einer Fachzeitschrift
(Review-Artikel)


Details zur Publikation

Autorinnen und Autoren: Fiebig P
Zeitschrift: Bulletin of the London Mathematical Society
Verlag: London Mathematical Society
Jahr der Veröffentlichung: 2010
Band: 42
Heftnummer: 6
Seitenbereich: 957-972
ISSN: 0024-6093


Abstract


We survey a new approach towards Lusztig's conjecture on the irreducible characters of a reductive algebraic group over a field of positive characteristic. The main result that we review is that Lusztig's conjecture is implied by a multiplicity conjecture on the stalks of certain sheaves on a moment graph. This latter conjecture is known to hold if the underlying field is of characteristic 0. From this one can almost directly deduce the conjecture for fields of large enough characteristics; but using a Lefschetz-type theory on the moment graph, we can give an upper bound on the exceptions. Moreover, one can prove the multiplicity 1 case of the conjecture in full generality. In addition to a survey of the above results, we prove the equivalence between the original conjecture of Lusztig and its generic version, that is, the multiplicity conjecture for baby Verma modules for the corresponding Lie algebra. © 2010 London Mathematical Society.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

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


Zitierweisen

APA:
Fiebig, P. (2010). Lusztig's conjecture as a moment graph problem. Bulletin of the London Mathematical Society, 42(6), 957-972. https://dx.doi.org/10.1112/blms/bdq058

MLA:
Fiebig, Peter. "Lusztig's conjecture as a moment graph problem." Bulletin of the London Mathematical Society 42.6 (2010): 957-972.

BibTeX: 

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