Branching Schubert calculus and the Belkale-Kumar product on cohomology

Nicolas Ressayre (1) , Edward Richmond (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Department of Mathematics, University of Oregon [Eugene]

In 2006, Belkale and Kumar define a new product on the cohomology of flag varieties and use 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.

Mots clés: Schubert calculus; Belkale-Kumar product

Domaines: Géométrie algébrique [math.AG]

Nicolas Ressayre, Edward Richmond. Branching Schubert calculus and the Belkale-Kumar product on cohomology. 2009. ⟨hal-00413516⟩