Mathematics – Representation Theory
Scientific paper
2010-12-09
Mathematics
Representation Theory
14 pages; minor edits in prep. for submission
Scientific paper
Braverman and Finkelberg have recently proposed a conjectural analogue of the geometric Satake isomorphism for untwisted affine Kac-Moody groups. As part of their model, they conjecture that (at dominant weights) Lusztig's q-analog of weight multiplicity is equal to the Poincare series of the principal nilpotent filtration of the weight space, as occurs in the finite-dimensional case. We show that the conjectured equality holds for all affine Kac-Moody algebras if the principal nilpotent filtration is replaced by the principal Heisenberg filtration. The main body of the proof is a Lie algebra cohomology vanishing result. We also give an example to show that the Poincare series of the principal nilpotent filtration is not always equal to the q-analog of weight multiplicity. Finally, we give some partial results for indefinite Kac-Moody algebras.
No associations
LandOfFree
A Brylinski filtration for affine Kac-Moody algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Brylinski filtration for affine Kac-Moody algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Brylinski filtration for affine Kac-Moody algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-77722