Singularities of Richardson varieties

TL;DR

This paper simplifies the study of singularities in Richardson varieties by reducing the problem to the well-understood case of Schubert varieties, leading to new and existing results.

Contribution

It provides a concise proof that links Richardson and Schubert varieties' singularity questions, streamlining future research.

Findings

Singularities of Richardson varieties can be analyzed through Schubert varieties.

New results on Richardson varieties' singularities are derived.

Previously known results are confirmed using the new approach.

Abstract

We give a short proof that essentially all questions concerning singularities of Richardson varieties reduce to corresponding questions about Schubert varieties. Consequently, we quickly deduce some new and previously known results.