A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Yao-Zhong Zhang; Mark D. Gould

doi:10.1063/1.1812829

paper

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

arXiv:math/0405043 · doi:10.1063/1.1812829

Abstract

Representations of the non-semisimple superalgebra $g l (2∣2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of $g l (2∣2)$ are constructed explicitly through the explicit construction of all $g l (2) \oplus g l (2)$ particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of $g l (2∣2)$ in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

LaTex file, 23 pages, two references and a comment added, to appear in J. Math. Phys