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

We provide an $\mathrm{E}\mathrm{x}\mathrm{t}$-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.