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arXiv · 2410.15538

The category $\bcalNT:$ Isomorphism criteria and applications

Diego Lobos
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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.

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Diego Lobos. 2024-10-20. The category $\bcalNT:$ Isomorphism criteria and applications. https://arxiv.org/abs/2410.15538

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