Nil graded algebras associated to triangular matrices and their applications to Soergel Calculus

TL;DR

This paper introduces a new class of nil graded algebras linked to Gelfand-Tsetlin subalgebras of Bott-Samelson bimodules, providing techniques for their optimal presentations within Soergel calculus.

Contribution

It develops a framework for nil graded algebras associated with triangular matrices and applies it to enhance understanding of Gelfand-Tsetlin subalgebras in Soergel calculus.

Findings

Established a connection between nil graded algebras and Gelfand-Tsetlin subalgebras

Developed techniques for optimal algebra presentations

Enhanced diagrammatic understanding in Soergel calculus

Abstract

We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain optimal presentations for the many Gelfand-Tsetlin subalgebras appearing in the context of the Diagrammatic Soergel Category.