Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations

TL;DR

This paper establishes a connection between equivariant tilting modules and derived categories of noncommutative resolutions of Pfaffian varieties, linking algebraic and geometric structures via derived factorization categories.

Contribution

It introduces a method using equivariant tilting modules to relate derived categories of noncommutative resolutions to derived factorization categories of gauged Landau-Ginzburg models.

Findings

Derived equivalences via equivariant tilting modules.

Noncommutative resolutions of Pfaffian varieties are linked to gauged Landau-Ginzburg models.

Explicit construction of derived category equivalences for linear sections.

Abstract

We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged Landau-Ginzburg model $(\Lambda,\chi, w)^{\mathbb{G}_m}$, where $\Lambda$ is a noncommutative resolution of the quotient singularity $W/\operatorname{GSp}(Q)$ arising from a certain representation $W$ of the symplectic similitude group $\operatorname{GSp}(Q)$ of a symplectic vector space $Q$.