Moduli of bundles and semiorthogonal decomposition

TL;DR

This paper develops a new semiorthogonal decomposition framework for moduli spaces of principal bundles on curves, utilizing advanced representation theory and geometric techniques.

Contribution

It introduces a novel semiorthogonal decomposition of moduli stacks and spaces of principal bundles, combining Borel-Weil-Bott theory, derived stratification, and Kac-Moody localization.

Findings

Decomposition of moduli stacks into symmetric powers.

Application of loop group representation theory.

Integration of derived stratification methods.

Abstract

In this paper we construct semiorthogonal decompositions of moduli of principal bundles on a curve into its symmetric powers, for both the moduli stack of all $G$-bundles and the coarse moduli space of semistable $G$-bundles. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, highest weight structure of current group representation, derived $\Theta$-stratification and local-global compatibility of Kac-Moody localization.