Some combinatorial aspects of generalised Bott-Samelson varieties

TL;DR

This paper presents combinatorial results related to Weyl groups and roots in the context of generalized Bott-Samelson varieties, aiding the understanding of rational curves and lines on Schubert varieties.

Contribution

It introduces new combinatorial equalities and inequalities in the setting of generalized Bott-Samelson resolutions of minuscule Schubert varieties.

Findings

Equality of Weyl groups established

Inequality of roots demonstrated

Application to minimal rational curves and lines on Schubert varieties

Abstract

We obtain two combinatorial results: an equality of Weyl groups and an inequality of roots, in the setting of generalised Bott-Samelson resolutions of minuscule Schubert varieties. These results are used in the companion paper [BK19] to describe minimal rational curves on these resolutions, and their relation to lines on the Schubert varieties.