# 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}
}
• 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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## References

SHOWING 1-10 OF 10 REFERENCES

### Eigenvalue problem and a new product in cohomology of flag varieties

• Mathematics
• 2004
Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenous

### The Belkale-Kumar cup product and relative Lie algebra cohomology

• Mathematics
• 2011
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### Cohomology Theory of Lie Groups and Lie Algebras

• Mathematics
• 1948
The present paper lays no claim to deep originality. Its main purpose is to give a systematic treatment of the methods by which topological questions concerning compact Lie groups may be reduced to

### An introduction to homological algebra

Preface 1. Generalities concerning modules 2. Tensor products and groups of homomorphisms 3. Categories and functors 4. Homology functors 5. Projective and injective modules 6. Derived functors 7.

### Lie Algebra Cohomology and Generalized Schubert Cells

This paper is referred to as Part II. Part I is [4], The numerical I used as a reference will refer to that paper. A third and final part, Clifford algebras and the intersection of Schubert cycles is

### Lie Algebra Cohomology and the Generalized Borel-Weil Theorem

The present paper will be referred to as Part I. A subsequent paper entitled, “Lie algebra cohomology and generalized Schubert cells,” will be referred to as Part II.

### Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups

• Mathematics
• 1999
The Description for this book, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), will be forthcoming.

• Springer,
• 2002

### discrete subgroups

• and representations of reductive groups, second ed., Mathematical Surveys and Monographs, vol. 67, American Mathematical Society, Providence, RI,
• 2000