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

Authors:
Sam Evens and William Graham

Journal:
Trans. Amer. Math. Soc. **365** (2013), 5833-5857

MSC (2010):
Primary 17B56, 14M15, 20G05

DOI:
https://doi.org/10.1090/S0002-9947-2013-05792-3

Published electronically:
August 2, 2013

MathSciNet review:
3091267

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Belkale-Kumar cup product on for a generalized flag variety with parameter , where . For each , we define an associated parabolic subgroup . We show that the ring contains a graded subalgebra isomorphic to with the usual cup product, where is a parabolic subgroup associated to the parameter . Further, we prove that is the quotient of the ring with respect to the ideal generated by elements of positive degree of . 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.

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Additional Information

**Sam Evens**

Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Email:
sevens@nd.edu

**William Graham**

Affiliation:
Department of Mathematics, University of Georgia, Boyd Graduate Studies Research Center, Athens, Georgia 30602

Email:
wag@math.uga.edu

DOI:
https://doi.org/10.1090/S0002-9947-2013-05792-3

Received by editor(s):
January 1, 2012

Published electronically:
August 2, 2013

Additional Notes:
The first author was supported by the National Security Agency

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.