Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians · arXivDesk
1511.04111Nov 12, 2015This 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
Diagrammatic description for the categories of perverse sheaves on isotropic Grassmannians
For each integer k≥4 we describe diagrammatically a positively graded Koszul algebra Dk such that the category of finite dimensional Dk
Nearby in the stack
-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type
Dk
or
Bk−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.