Branching Schubert calculus and the Belkale-Kumar product on cohomology

TL;DR

This paper generalizes the Belkale-Kumar product to branching Schubert calculus, providing a compact formulation for solving the branching eigencone problem in the cohomology of flag varieties.

Contribution

It introduces a new product on cohomology in the branching Schubert calculus setting, extending the Belkale-Kumar product to address the branching eigencone problem.

Findings

Generalized Belkale-Kumar product for branching Schubert calculus

Compact formulation of the branching eigencone problem

Enhanced understanding of cohomology maps in flag variety embeddings

Abstract

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.