Kempf-Ness type theorems and Nahm equations

TL;DR

This paper extends the Kempf-Ness theorem to non-algebraic symplectic structures and applies it to describe hyperkähler quotients of the cotangent bundle of a complex reductive group, broadening the theorem's applicability.

Contribution

It proves a version of the affine Kempf-Ness theorem for non-algebraic symplectic structures and uses it to analyze hyperkähler quotients of T*G.

Findings

Extended Kempf-Ness theorem to non-algebraic settings

Described hyperkähler quotients of T*G using the new theorem

Connected symplectic geometry with hyperkähler quotient construction

Abstract

We prove a version of the affine Kempf-Ness theorem for non-algebraic symplectic structures and shifted moment maps, and use it to describe hyperkahler quotients of T*G, where G is a complex reductive group.