Micu-type invariants for the Casimir operators of the Lie superalgebras osp(1,2n): application to the algebra osp(1,4)

Abstract

A construction of the Casimir operators of higher degree of the Lie superalgebras osp(1,2n) by a method which represents a generalisation of the method proposed by Micu for the construction of the Casimir operators of the Lie algebras, namely the algebras Sp(2n), is suggested. The method applied has a close connection with Backhouse's method of construction of Casimir operators for the semisimple Lie superalgebras. Above all the fourth-order coefficients of the Casimir operators of superalgebras osp(1,2n) are shown to play a determining role for the Casimir operators of higher degrees.