Quantisation of U$_q$[OSP(1/2N)] with Deformed Para-Bose Operators

TL;DR

This paper develops a quantum deformation of para-Bose operators related to the orthosymplectic Lie superalgebra, providing a new operator framework and algebraic relations for $U_q[osp(1/2n)]$, including a PBW-type theorem.

Contribution

It introduces deformed para-Bose operators as an alternative to Chevalley generators for $U_q[osp(1/2n)]$, and formulates its algebraic structure and PBW theorem.

Findings

Deformed para-Bose operators generate $U_q[osp(1/2n)]$.

Explicit algebraic relations in terms of deformed pB operators.

Formulation of an analog of the PBW theorem for the deformed algebra.

Abstract

The observation that $n$ pairs of para-Bose (pB) operators generate the universal enveloping algebra of the orthosymplectic Lie superalgebra $osp(1/2n)$ is used in order to define deformed pB operators. It is shown that these operators are an alternative to the Chevalley generators. On this background $U_q[osp(1/2n)]$, its "Cartan-Weyl" generators and their "supercommutation" relations are written down entirely in terms of deformed pB operators. An analog of the Poincare- Birkhoff-Witt theorem is formulated.