A supercoherent state and a new inhomogeneous differential realization of the \(\text{spl}(2,1)\) superalgebra (Q5944694)

It is known that the key to the settlement of the quasi-exactly solvable problems lies in studing finite dimensional inhomogeneous differential realization of Lie (super)algebra. Therefore it is important to study the cohorent state and inhomogeneous differential realization of Lie superalgebras. The purpose of this paper is to derive a new inhomogeneous differential realization of the \(\text{spl}(2,1)\) Lie superalgebra on the basis of studing the supercoherent state. The author has constructed the supercoherent state of the \(\text{spl}(2,1)\) superalgebra and he has discussed its properties in detail. Finally a new form of the inhomogeneous differential realizations of the \(\text{spl}(2,1)\) in supercoherent state are given.