A class of perverse schobers in Geometric Invariant Theory

TL;DR

This paper constructs a perverse schober on a partial compactification of the stringy K"ahler moduli space, extending previous local systems of categories associated with quasi-symmetric representations of reductive groups.

Contribution

It introduces a new perverse schober structure on the SKMS related to quasi-symmetric representations, expanding the categorification framework in geometric invariant theory.

Findings

Constructed a perverse schober extending existing local systems.

Connected the schober to subcategories of derived categories of quotient stacks.

Provides a new categorification perspective in GIT moduli spaces.

Abstract

Perverse schobers are categorifications of perverse sheaves. We construct a perverse schober on a partial compactification of the stringy K\"ahler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation X of a reductive group G, extending the local system of triangulated categories established by them. The triangulated categories appearing in our perverse schober are subcategories of the derived category of the quotient stack X/G.