Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians

Abstract

For each integer $k\ge 4$ we describe diagrammatically a positively graded Koszul algebra ${\mathbb{D}}_k$ such that the category of finite dimensional ${\mathbb{D}}_k$-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type ${\mathrm{D}}_k$ or ${\mathrm{B}}_{k-1}$, constructible with respect to the Schubert stratification. The algebra is obtained by a (non-trivial) ``folding'' procedure from a generalized Khovanov arc algebra. Properties like graded cellularity and explicit closed formulas for graded decomposition numbers are established by elementary tools.

arXiv commentThis is an extended and generalized version of the first part of the previous paper entitled "Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n).", see arXiv:1306.4043 It also contains an an extra examples section