Deformed quantum Calogero-Moser problems and Lie superalgebras

TL;DR

This paper introduces deformed quantum Calogero-Moser problems linked to Lie superalgebras, establishing their integrability and analyzing their algebraic structures and Poincare series for various parameters.

Contribution

It constructs a new class of integrable quantum problems associated with Lie superalgebras using generalized root systems and derives explicit formulas for their quantum integrals.

Findings

Recurrent formula for quantum integrals established

Proved integrability of the deformed problems

Explicit Poincare series formulas derived

Abstract

The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized root systems suggested by V. Serganova. For the classical series a recurrent formula for the quantum integrals is found, which implies the integrability of these problems. The corresponding algebras of the quantum integrals are investigated, the explicit formulas for their Poincare series for generic values of the deformation parameter are presented.