Monodromy for systems of vector bundles and multiplicative preprojective algebras

TL;DR

This paper establishes a monodromy functor connecting systems of vector bundles with logarithmic connections on Riemann surfaces to representations of multiplicative preprojective algebras, generalizing classical algebraic structures.

Contribution

It introduces a monodromy functor for systems involving vector bundles and logarithmic connections, extending the framework of deformed preprojective algebra representations.

Findings

Existence of a monodromy functor linking systems to multiplicative preprojective algebra representations

Isomorphism between multiplicative and usual preprojective algebras for Dynkin quivers

Generalization of representation theory of deformed preprojective algebras

Abstract

We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence of a monodromy functor from such systems to representations of a multiplicative preprojective algebra. As a corollary, we prove that the multiplicative preprojective algebra associated to a Dynkin quiver is isomorphic to the usual preprojective algebra.