Associated graded of Hodge modules and categorical sl₂ actions

2016/03/24 by Sabin Cautis, Cautis, Sabin, C. A. F. Dodd +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1603.07402

openalex publication_date 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One of the most mysterious aspects of Saito's theory of Hodge modules are the Hodge and weight filtrations that accompany the pushforward of a Hodge module under an open embedding. In this paper we consider the open embedding in a product of complementary Grassmannians given by pairs of transverse subspaces. The push-forward of the structure sheaf under this open embedding is an important Hodge module from the viewpoint of geometric representation theory and homological knot invariants. We compute the associated graded of this push-forward with respect to the induced Hodge filtration as well as the resulting weight filtration. The main tool is a categorical \sl₂ action on the category of \D_h-modules on Grassmannians. Along the way we also clarify the interaction of kernels for \D_h-modules with the associated graded functor. Both of these results may be of independent interest.

Citations

• Etingof conjecture for quantized quiver varieties
• 2-Kac-Moody algebras

Cited by

• Categorification via blocks of modular representations for sl(n)

Related

• Local cohomology with support in Schubert varieties
• K-theory of moduli spaces of sheaves and large Grassmannians
• Characteristic classes of mixed Hodge modules
• Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions
• The Hodge realization functor on the derived category of relative motives