2012/01/01 by Sam Evens, Evens, Sam, William Graham +1
Mathematics · #14M15 #17B56 #20G05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14M15 #msc:17B56 #msc:20G05
paper · pdf · doi:10.48550/arxiv.1201.0380
arxiv created 2012/01/01 · openalex publication_date 2012/01/01 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Belkale-Kumar cup product \odott on H^*(G/P) for a generalized flag variety G/P with parameter t ∈ \Cm, where m=dim(H2(G/P)). For each t∈ \Cm, we define an associated parabolic subgroup PK ⊃ P. We show that the ring (H^*(G/P), \odott) contains a graded subalgebra A isomorphic to H^*(PK/P) with the usual cup product, where PK is a parabolic subgroup associated to the parameter t. Further, we prove that (H^*(G/PK), \odot0) is the quotient of the ring (H^*(G/P), \odott) with respect to the ideal generated by elements of positive degree of A. We prove the above results by using basic facts about the Hochschild-Serre spectral sequence for relative Lie algebra cohomology, and most of the paper consists of proving these facts using the original approach of Hochschild and Serre.