The category $\bcalNT:$ Isomorphism criteria and applications

TL;DR

This paper develops isomorphism criteria for the category alNT, aiding the structural understanding of Gelfand-Tsetlin subalgebras within the diagrammatic Soergel category, with applications to algebraic and categorical analysis.

Contribution

It introduces new isomorphism criteria for alNT, facilitating the study of Gelfand-Tsetlin subalgebras in diagrammatic categorification.

Findings

Established criteria for isomorphisms in alNT

Applied criteria to analyze Gelfand-Tsetlin subalgebras

Enhanced understanding of algebraic structures in diagrammatic categories

Abstract

The category $\bcalNT$ was introduced in \cite{Lobos2} in order to provide a structural setting to the study of the many Gelfand-Tsetlin subalgebras appearing in the context of the diagrammatic Soergel category of Elias and Williamson \cite{EW}. The category $\bcalNT$ have as objects, all that we called \emph{nil graded algebras associated to a triangular matrix} and as morphisms, all the \emph{preserving degree} homomorphisms of graded algebras between them. In this article we develop a series of \emph{isomorphism criteria} on $\bcalNT$ that we used later to find out relevant information on the Gelfand-Tsetlin subalgebras of the diagrammatic Soergel category.