Highest weights for truncated shifted Yangians and product monomial crystals

TL;DR

This paper explores the highest weight representations of truncated shifted Yangians, proposing a conjecture that these weights are characterized by product monomial crystals, and confirms this in type A, linking to symplectic duality.

Contribution

It introduces a conjecture relating highest weights of truncated shifted Yangians to product monomial crystals and proves it in type A, connecting to symplectic duality and Hikita's conjecture.

Findings

Conjecture that highest weights are described by product monomial crystals

Proof of the conjecture in type A

Connection established with symplectic duality and Hikita's conjecture

Abstract

Truncated shifted Yangians are a family of algebras which are natural quantizations of slices in the affine Grassmannian. We study the highest weight representations of these algebras. In particular, we conjecture that the possible highest weights for these algebras are described by product monomial crystals, certain natural subcrystals of Nakajima's monomials. We prove this conjecture in type A. We also place our results in the context of symplectic duality and prove a conjecture of Hikita in this situation.