Finite-dimensional representations of the Lie superalgebra sl(1,3) in a Gel’fand–Zetlin basis. I. Typical representations

Abstract

In a series of two papers all finite-dimensional irreducible representations of the special linear Lie superalgebra sl(1,3) are constructed. Explicit formulas for the generators in an orthonormal Gel’fand–Zetlin basis of the even subalgebra gl(3) are given. This paper develops a background for constructing the representations. Expressions for the transformation properties of the basis under the action of the generators are written down within all typical sl(1,3) modules.