The Belkale-Kumar cup product and relative Lie algebra cohomology
Algebraic Geometry
2011-05-30 v2 Representation Theory
Abstract
We study the Belkale-Kumar family of cup products on the cohomology of a generalized flag variety. We give an alternative construction of the family using relative Lie algebra cohomology, and in particular, identify the Belkale-Kumar cup product with a relative Lie algebra cohomology ring for every value of the parameter. As a consequence, we extend a fundamental disjointness result of Kostant to a family of Lie algebras. In an appendix, written jointly with Edward Richmond, we extend a Levi movability result of Belkale and Kumar to arbitrary parameters.
Keywords
Cite
@article{arxiv.1104.1415,
title = {The Belkale-Kumar cup product and relative Lie algebra cohomology},
author = {Sam Evens and William Graham and with an appendix jointly written with Edward Richmond},
journal= {arXiv preprint arXiv:1104.1415},
year = {2011}
}
Comments
26 pages; some small revisions from previous version