Separation of variables for symplectic characters

TL;DR

This paper applies Sklyanin's separation of variables scheme to symplectic Weyl characters, constructing explicit operators and Hamiltonians within a quantum integrable system framework.

Contribution

It introduces a novel method for separating variables in symplectic characters using the Q-operator approach, providing explicit constructions of operators and Hamiltonians.

Findings

Explicit separating operator constructed for symplectic characters

Inverse of the separating operator explicitly derived

Factorised Hamiltonian explicitly obtained

Abstract

We perform separation of variables for the symplectic Weyl character using Sklyanin's scheme. Viewing the characters as eigenfunctions of a quantum integrable system, we explicitly construct the separating operator using the Q-operator method. We also construct the inverse of the separating operator, as well as the factorised Hamiltonian.