Lusztig's conjecture as a moment graph problem

Details Lusztig's conjecture as a moment graph problem Lusztig's conjecture as a moment graph problem

2007-12-23

arxiv.org/abs/0712.3909v4

Bull. London Math. Soc. (2010) 42(6): 957-972

Mathematics

Representation Theory

17 pages; revised version with minor changes

Scientific paper

10.1112/blms/bdq058

We show that Lusztig's conjecture on the irreducible characters of a reductive algebraic group over a field of positive characteristic is equivalent to the generic multiplicity conjecture, which gives a formula for the Jordan-H"older multiplicities of baby Verma modules over the corresponding Lie algebra. Then we give a short overview of a recent proof of the latter conjecture for almost all base fields via the theory of sheaves on moment graphs.

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