Algebraic spectral relations for elliptic quantum Calogero-Moser problems

TL;DR

This paper derives explicit algebraic relations between quantum integrals for elliptic Calogero-Moser problems associated with specific root systems, advancing understanding of their algebraic structure.

Contribution

It provides the first explicit algebraic relations between quantum integrals for elliptic Calogero-Moser problems related to root systems A2 and B2.

Findings

Explicit algebraic relations for A2 and B2 systems

Enhanced understanding of quantum integrals in elliptic Calogero-Moser models

Foundational step for further algebraic analysis of integrable systems

Abstract

Explicit algebraic relations between the quantum integrals of the elliptic Calogero--Moser quantum problems related to the root systems ${\bf A_2}$ and ${\bf B_2}$ are found.