Langlands parameters of quivers in the Sato Grassmannian

TL;DR

This paper explores the connection between quivers in the Sato Grassmannian and geometric Langlands parameters, linking quantum field theory, integrable systems, and algebraic geometry.

Contribution

It introduces new methods to attach geometric Langlands parameters to quivers in the Sato Grassmannian and studies their properties and limits.

Findings

Establishment of local geometric Langlands parameters for quivers

Analysis of Virasoro constraints related to these quivers

Insights into classical limits of the Langlands parameters

Abstract

Motivated by quantum field theoretic partition functions that can be expressed as products of tau functions of the KP hierarchy we attach several types of local geometric Langlands parameters to quivers in the Sato Grassmannian. We study related questions of Virasoro constraints, of moduli spaces of relevant quivers, and of classical limits of the Langlands parameters.