Quantum integrability of the deformed elliptic Calogero-Moser problem

The integrability of the deformed quantum elliptic Calogero-Moser problem introduced by Chalykh, Feigin and Veselov is proven. Explicit recursive formulae for the integrals are found. For integer values of the parameter this implies the algebraic integrability of the systems.Comment: 23 page

On algebraic integrability of the deformed elliptic Calogero--Moser problem

Algebraic integrability of the elliptic Calogero--Moser quantum problem related to the deformed root systems \pbf{A_{2}(2)} is proved. Explicit formulae for integrals are found

A and Prikhodsky I A, Algebraic Spectral Relations for Elliptic Quantum Calogero–Moser Problems

Explicit algebraic relations between the quantum integrals of the elliptic Calogero– Moser quantum problems related to the root systems A2 and B2 are found.