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Diego Lobos

Publications and source records attributed to Diego Lobos.

6 recordsLinked to original sources
arXiv2025

On finitude of the number of isomorphism classes in the category NT

The category $\bcalNT$ was defined in \cite{Lobos2}, it is a category whose objects are commutative nil graded algebras over a field, defined by presentation encoded by triangular matrices. A natural problem related to this category is to reach a complete classification up to isomorphism of its objects. Based in some results coming from \cite{Lobos2}, we can divide this problem by working with encoding matrices of a fixed size $n.$ In \cite{Lobos3} and \cite{Lobos4}, there are several advances for this search, in particular, in \cite{Lobos3} one can see that, for small matrices, the number of isomorphism classes seems to be finite and independent on the ground field. That fact, opened a series of questions related with the number of isomorphism classes and its relation with the ground field. At that point it was no clear, under which conditions of the ground field, this number could be finite. In this article, among other results, we prove that for each $n\geq4,$ the number of isomorphism classes is finite if and only if the ground field is finite.

math.AC↗
arXiv2025

Framed Blob Monoids

We introduce and study blob and framed blob monoids. In particular, several realizations of these monoids are given. We compute the cardinality of the framed blob monoid and derive some combinatorial formulas involving this cardinality.

math.CO↗
arXiv2024

The category $\bcalNT:$ Isomorphism criteria and applications

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.

math.RT↗
arXiv2020

The nil-blob algebra: An incarnation of type $\tilde{A}_1$ Soergel calculus and of the truncated blob algebra

We introduce a type $B$ analogue of the nil Temperley-Lieb algebra in terms of generators and relations, that we call the (extended) nil-blob algebra. We show that this algebra is isomorphic to the endomorphism algebra of a Bott-Samelson bimodule in type $\tilde{A}_1$. We also prove that it is isomorphic to an idempotent truncation of the classical blob algebra.Thus we provide strong evidence in favor of the recent Blob vs. Soergel conjecture.

math.RT↗
arXiv2019

Graded cellular basis and Jucys-Murphy elements for generalized blob algebras

We give a concrete construction of a graded cellular basis for the generalized blob algebra B_n introduced by Martin and Woodcock. The construction uses the isomorphism between KLR-algebras and cyclotomic Hecke algebras, proved by Brundan-Kleshchev and Rouquier. It gives rise to a family of Jucys-Murphy elements for B_n.

math.RT↗