One-Parameter Indecomposable Representation of SPL(2,1) Superalgebra

Using inhomogeneous boson–fermion realization one-parameter indecomposable representation of the SPL(2,1) superalgebra is studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg-Weyl superalgebra. PACS: 12.60.Jv; 03.65.FdThe author was supported financially by Shenzhen Institute of Information Technology.     

One-Parameter Irreducible Representation of spl(2,1) Superalgebra

One-parameter irreducible representation of the spl(2,1) superalgebra is studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg-Weyl superalgebra. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons. The author was supported financially by Shenzhen science and technology plan project and Shenzhen Institute of Information Technology Grant No. szkj0711.     

One-Parameter General Coherent State of the gl(2,1) Superalgebra

One-parameter general coherent state of the gl(2,1) superalgebra is constructed. Its properties are discussed in detail. One-parameter matrix elements of the gl(2,1) generators in the one-parameter general coherent-state space are calculated.     

On One-Parameter Supercoherent State Representation of the gl(2,1) Superalgebra

One-parameter supercoherent state of the gl(2,1) superalgebra is constructed. Its properties are discussed in detail. An arbitrary vector can be expanded in terms of the supercoherent state for the gl(2,1) superalgebra.     

One-Parameter Inhomogeneous Differential Realizations and Boson–Fermion Realizations of the gl(2¦1) Superalgebra

One-parameter homogeneous and inhomogeneous differential realizations of the gl(2¦1) superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson–fermion realizations are studied. The parameter has relation to the Hubbard interaction parameter U in the Hubbard model for correlated electrons.     

Irreducible Representations of Quantum Lie Superalgebra SLq(2/1)

In this paper,some generators of SL_q(2/1),satisfying the Serre-like relations,can be considered as 1/2 rank tensor-like operators.The reduced matrix elements of them can be calculated by a set of recurrent formula.Thus th irreducible representations of SL_q(2/1) may be completely determined.     

Quantum Affine Superalgebra Uq(gl(1|1)) and Its

Drinfeld's realization of quantum affine superalgebra U_q(gl(1|1)) is given based on the super version of RS construction method and Gauss decomposition.     

SPL(2，1)超代数的不可分解表示和不可约表示

利用ＳＰＬ（２,１）的非齐次玻色 费米实现,研究了ＳＰＬ（２,１）在Ｈｅｉｓｅｎｂｅｒｇ Ｗｅｙｌ超代数的广义包络代数的子空间和商空间上的不可分解表示和不可约表示,并给出了它的全部有限维不可约表示 关键词：     

The Paraboson Fock Space and Unitary Irreducible Representations of the Lie Superalgebra {\mathfrak{osp}(1|2n)}

It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters. NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). An erratum to this article can be found at     

Coherent State Representations of Lie Superalgebra SU(2/1)

We present a kind of new coherent states associated with the Lie superalgebra SU(2/1), and discuss their properties in detail. We also evaluate the matrix elements of the SU(2/1) generators in the coherent state representations and obtain differential realizations of the SU(2/1) algebra in the coherent state space. The differential realizations may be useful for the study of the quasi-exactly solvable problems in the quantum mechanics.     

The Embedding of Quantum Algebra U(gl(n+1)) in Irreducible Representations of U(gl(n+1))

Using a formula derived by Jimbo, we express the generators of U(gl(n+1)), the q-analogue of U(gl(n+1)) in an irreducible representation with Gel'fand basis, as functions of the generators of U(gl(n+1)).     

Indecomposable Representations of the Quantum Group SU(2)q1

The infinite-dimensional indecomposable representations are constructed by using the purely algebraic method and the matrix elements for these representations are obtained in an explicit form. Each familiar finite-dimensional irreducible representation ia induced on a quotient space.     

On One-Parameter Supercoherent State of spl(2,1) Superalgebra

One-Parameter supercoherent state of the spl(2,1) superalgebra is constructed and its properties are discussed in detail. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons. The author was supported financially by Shenzhen science and technology plan project and Shenzhen Institute of Information Technology Grant No. szkj0711.     

On Characters and Superdimensions of Some Infinite-Dimensional Irreducible Representations of osp(m|n)

Physics of Atomic Nuclei - Chiral spinors and self dual tensors of the Lie superalgebra osp(m|n) are infinite-dimensional representations belonging to the class of representations with Dynkin...     

One-Parameter Inhomogeneous Differential Realization and Boson-Fermion Realization of the SPL(2,1) Superalgebra

One-parameter inhomogeneous differential realization of the SPL(2,1) superalgebra on the space of homogeneous polynomials and the corresponding boson-fermion realization are studied. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.     

Boundary Correlation Functions of the gl(1|1) Supersymmetric Vertex Model

The gl(1|1) supersymmetric vertex model with domain wall boundary conditions (DWBC) on an N×N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.