Branching Schubert calculus and the Belkale-Kumar product on cohomology

Ressayre, Nicolas; Richmond, Edward

doi:10.1090/S0002-9939-2010-10681-0

Branching Schubert calculus and the Belkale-Kumar product on cohomology
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by Nicolas Ressayre and Edward Richmond PDF

Proc. Amer. Math. Soc. 139 (2011), 835-848 Request permission

Abstract:

In 2006 Belkale and Kumar defined a new product on the cohomology of flag varieties and used this new product to give an improved solution to the eigencone problem for complex reductive groups. In this paper, we give a generalization of the Belkale-Kumar product to the branching Schubert calculus setting. The study of branching Schubert calculus attempts to understand the induced map on cohomology of an equivariant embedding of flag varieties. The main application of our work is a compact formulation of the solution to the branching eigencone problem.

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