Khovanov-Lauda-Rouquier subalgebras and redotted Webster algebras

TL;DR

This paper introduces generalized Khovanov-Lauda-Rouquier subalgebras that extend Webster's tensor product algebras, establishing isomorphisms with quotient algebras in various types.

Contribution

It defines new subalgebras generalizing redotted Webster algebras and proves their quotient algebras are isomorphic to Webster's tensor product algebras across different types.

Findings

Defined Khovanov-Lauda-Rouquier subalgebras as generalizations.

Proved quotient algebras are isomorphic to Webster's tensor product algebras.

Extended the framework to general types.

Abstract

We define Khovanov-Lauda-Rouquier subalgebras which are generalizations of redotted versions of Webster's tensor product algebras of type $A_1$. Quotient algebras of these subalgebras are isomorphic to Webster's tensor product algebras in general type.