Cosmall Roots and Curve Neighborhoods

TL;DR

This paper proves a conjecture about P-cosmall roots in the context of Schubert varieties and provides explicit combinatorial criteria for identifying these roots.

Contribution

It confirms a conjecture on P-cosmall roots and offers explicit combinatorial conditions for their identification.

Findings

Proof of the conjecture regarding P-cosmall roots

Explicit combinatorial criteria for P-cosmall roots

Enhanced understanding of curve neighborhoods in Schubert varieties

Abstract

A previous result in a paper by Buch and Mihalcea relates the curve neighborhood of any Schubert variety to the curve neighborhood of a point and introduces the idea of P-cosmall roots. In our paper, we prove a conjecture given in that same paper about P-cosmall roots. We go on to provide explicit combinatorial conditions for a root to be P-cosmall.