A family of reductions for Schubert intersection problems

TL;DR

This paper introduces a family of reduction techniques for Schubert intersection problems that preserve key coefficients and facilitate explicit solutions when the coefficient equals one.

Contribution

It presents a novel set of reductions for Schubert intersection problems that maintain Littlewood-Richardson coefficients and enable explicit solutions in specific cases.

Findings

Reductions do not change Littlewood-Richardson coefficients.

Explicit solutions are obtained when the coefficient is 1.

Reductions are verified via linear dimension calculations.

Abstract

We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions do not alter the Littlewood-Richardson coefficient, and they lead to an explicit solution of the intersection problem when this coefficient is 1.