Degenerate integrability of quantum spin Calogero--Moser systems

TL;DR

This paper proves the degenerate quantum integrability of quantum spin Calogero--Moser systems and describes their spectrum using Lie algebra representation theory.

Contribution

It establishes the degenerate quantum integrability of these systems and links the spectrum to tensor product decompositions of Lie algebra representations.

Findings

Quantum spin Calogero--Moser systems are degenerate integrable.

Spectrum characterized by Lie algebra tensor product decompositions.

Provides a representation-theoretic description of quantum Hamiltonians.

Abstract

The main result of this note is the proof of degenerate quantum integrability of quantum spin Calogero--Moser systems and the description of the spectrum of quantum Hamiltonians in terms of the decomposition of tensor products of irreducible representations of corresponding Lie algebra.