Intersection multiplicity one for classical groups

TL;DR

This paper proves that for classical semi-simple algebraic groups, the structure coefficients of a specific cohomology product are always either 0 or 1, revealing a simple multiplicity structure.

Contribution

It establishes that the structure coefficients of the Belkale-Kumar product on cohomology are binary (0 or 1) for classical groups, simplifying understanding of their algebraic structure.

Findings

Structure coefficients are always 0 or 1.

Results apply to classical semi-simple algebraic groups.

Simplifies the understanding of cohomology products.

Abstract

In this paper we show that when $\mathrm{G}$ is a classical semi-simple algebraic group, $\mathrm{B}\subset\mathrm{G}$ a Borel subgroup, and $\mathrm{X} = \mathrm{G}/\mathrm{B}$, then the structure coefficients of the Belkale-Kumar product $\odot_{0}$ on $\mathrm{H}^{*}(\mathrm{X}, \mathbf{Z})$ are all either $0$ or $1$.