Quiver presentations and isomorphisms of Hecke categories and Khovanov arc algebras

TL;DR

This paper establishes an isomorphism between extended Khovanov arc algebras and basic algebras of anti-spherical Hecke categories for symmetric groups, providing explicit quiver presentations and submodule structures.

Contribution

It introduces a new isomorphism linking Khovanov arc algebras with Hecke categories, with explicit algebraic and module-theoretic descriptions.

Findings

Proves isomorphism between Khovanov arc algebras and Hecke category algebras

Provides quiver and relations for these algebras

Describes submodule lattices of Verma modules

Abstract

We prove that the extended Khovanov arc algebras are isomorphic to the basic algebras of anti-spherical Hecke categories for maximal parabolics of symmetric groups. We present these algebras by quiver and relations and provide the full submodule lattices of Verma modules.