A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)
نویسندگان
چکیده
Representations of the non-semisimple superalgebra gl(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 gl(2|2) are constructed explicitly through the explicit construction of all gl(2)⊕ gl(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 gl(2|2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.
منابع مشابه
Explicit Representations of Classical Lie Superalgebras in a Gelf
Abstract. An explicit construction of all finite-dimensional irreducible representations of classical Lie algebras is a solved problem and a Gelfand-Zetlin type basis is known. However the latter lacks the orthogonality property or does not consist of weight vectors for so(n) and sp(2n). In case of Lie superalgebras all finite-dimensional irreducible representations are constructed explicitly o...
متن کاملIrreducible Representations of U Pq [gl(2/2)]
The two–parametric quantum superalgebra U p,q [gl(2/2)] and its representations are considered. All finite–dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and non–typical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superal-gebra gl(2/2)...
متن کاملFinite-dimensional Irreducible Representations of Twisted Yangians
We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to the coproduct in Y(gl(N)). We give a complete description of their finite-dimensional irreducible representations. Every such representation is highest weight...
متن کاملSchur-Weyl reciprocity between the quantum superalgebra and the Iwahori-Hecke algebra
In the representation theory, the classification and the construction of the irreducible representations are essential themes. In the first half of the twentieth century, I. Schur[11] introduced a prominent method to obtain the finite dimensional irreducible representations of the general linear group GL(n,C), or equivalently of its Lie algebra gl(n,C), which we call Schur-Weyl reciprocity at p...
متن کاملPrimary Fields and Screening Currents of gl(2|2) Non-unitary Conformal Field Theory
The non-semisimple gl(2|2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(2|2) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten fr...
متن کامل