Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)

2013/06/17 by Michael Ehrig, Ehrig, Michael, Catharina Stroppel +1 · 1 citation
Mathematics · #05E10 #14M15 #17B10 #17B45 #20C08 #55N91 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1306.4043

openalex publication_date 2013/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe diagrammatically a positively graded Koszul algebra \mathbbD_k such that the category of finite dimensional \mathbbD_k-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type D_k constructible with respect to the Schubert stratification. The connection is given by an explicit isomorphism to the endomorphism algebra of a projective generator described in by Braden. The algebra is obtained by a "folding" procedure from the generalized Khovanov arc algebras. We relate this algebra to the category of finite dimensional representations of the orthosymplectic supergroups. The proposed equivalence of categories gives a concrete description of the categories of finite dimensional SOSP(m|2n)-modules.

Citations

• 2-Kac-Moody algebras

Cited by

• Geometric Schur Duality of two parameter quantum group of type A

Related

• Perverse sheaves on Grassmannians
• A diagram algebra for Soergel modules corresponding to smooth Schubert varieties
• Perverse sheaves, Koszul IC-modules, and the quiver for the category O
• Perverse sheaves on symmetric products of the plane
• Perverse sheaves and finite-dimensional algebras