2011/04/07 by Sam Evens, Evens, Sam, William Graham +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AG #math.RT #msc:14N15 #msc:14N35 #msc:17B56
paper · pdf · doi:10.48550/arxiv.1104.1415
26 pages; some small revisions from previous version
arxiv created 2011/05/27 · arxiv updated 2011/05/30
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.