Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians

TL;DR

This paper establishes a Hamiltonian reduction relationship between neighboring affine Grassmannian slices and extends this to their quantized versions, the truncated shifted Yangians, revealing new geometric and algebraic connections.

Contribution

It proves that neighboring affine Grassmannian slices are related via Hamiltonian reduction and extends this to their quantizations, the truncated shifted Yangians.

Findings

Neighboring affine Grassmannian slices are related by Hamiltonian reduction.

A weaker version of this relation holds for their quantizations, the truncated shifted Yangians.

Provides new insights into the geometric and algebraic structure of these objects.

Abstract

Generalized affine Grassmannian slices provide geometric realizations for weight spaces of representations of semisimple Lie algebras. They are also Coulomb branches, symplectic dual to Nakajima quiver varieties. In this paper, we prove that neighbouring generalized affine Grassmannian slices are related by Hamiltonian reduction by the action of the additive group. We also prove a weaker version of the same result for their quantizations, algebras known as truncated shifted Yangians.