Isotropic meta Kazhdan--Lusztig combinatorics I: Ext-quiver presentation for the Hecke category

TL;DR

This paper introduces a new algebraic presentation for the anti-spherical Hecke categories associated with isotropic Grassmannians, utilizing meta Kazhdan--Lusztig combinatorics and Temperley--Lieb diagrams.

Contribution

It provides an explicit Ext-quiver and relations for the basic algebra of these categories, connecting combinatorics with diagrammatic algebra.

Findings

Explicit Ext-quiver for the Hecke category

Relations derived from meta Kazhdan--Lusztig combinatorics

Diagrammatic presentation using Temperley--Lieb diagrams

Abstract

We provide an ${\rm Ext}$-quiver and relations presentation for the basic algebra of the anti-spherical Hecke categories of isotropic Grassmannians, $H_{(D_n, A_{n-1})}$, in terms of cup-cap meta Kazhdan--Lusztig combinatorics and Temperley--Lieb diagrammatics.