Inhomogeneous Differential Realization, Boson-Fermion Realization of Lie Superalgebra B(0,1) and its Representations

Abstract：

The differential realization of Lie superalgebra B(0,1) on the space of inhomogeneous polynomials (called inhomogeneous differential realization), and the corresponding inhomogeneous Boson-Fermion realization are studied. By making use of the inhomogeneous Boson-Fermion realization, a new kind of indecomposable and irreducible representation of Lie superalgebra B(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra, its subspaces and its quotient spaces; AH the finite dimensional irreducible representations of Lie superalgebra B(0,1) are naturally obtained as special cases.