Quiver presentations and Schur--Weyl duality for Khovanov arc algebras

TL;DR

This paper presents a quiver and relations presentation of Khovanov arc algebras and proves an analogue of the Kleshchev--Martin conjecture within this framework.

Contribution

It introduces an Ext-quiver and relations presentation for Khovanov arc algebras and establishes a conjecture analogue, advancing understanding of their algebraic structure.

Findings

Provided an explicit Ext-quiver and relations presentation.

Proved an analogue of the Kleshchev--Martin conjecture for these algebras.

Enhanced the algebraic understanding of Khovanov arc algebras.

Abstract

We provide an ${\rm Ext}$-quiver and relations presentation of the Khovanov arc algebras and prove a precise analogue of the Kleshchev--Martin conjecture in this setting.