Isotropic Meta Kazhdan-Lusztig Combinatorics II: Isomorphism to the generalised Khovanov arc algebra

Abstract

We construct an explicit isomorphism between the generalised Khovanov arc algebras of type D and the basic algebras of the anti-spherical Hecke category associated to the maximal parabolic subgroup $W(A_{n-1})$ of $W(Dn)$. This isomorphism maps generators to generators, thereby equipping the arc algebras with an Ext-quiver and relations presentation.

Update to include appendix explaining the small change of definition of the arc algebra and the effect on its associativity