The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product

@article{Evens2012TheRH,
  title={The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product},
  author={Sam Evens and William Graham},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={365},
  pages={5833-5857}
}
  • S. Evens, W. Graham
  • Published 1 January 2012
  • Mathematics
  • Transactions of the American Mathematical Society
We consider the Belkale-Kumar cup product $\odot_t$ on $H^*(G/P)$ for a generalized flag variety $G/P$ with parameter $t \in \C^m$, where $m=\dim(H^2(G/P))$. For each $t\in \C^m$, we define an associated parabolic subgroup $P_K \supset P$. We show that the ring $(H^*(G/P), \odot_t)$ contains a graded subalgebra $A$ isomorphic to $H^*(P_K/P)$ with the usual cup product, where $P_K$ is a parabolic subgroup associated to the parameter $t$. Further, we prove that $(H^*(G/P_K), \odot_0)$ is the… 
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