The Boundary States of the q-Deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U_q[\widehat{sl(2|1)}]. We give the bosonization of the boundary states.     

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.     

Irreducible Representations of the Quantum Group Uq(m + n) in Uq(m)⊕ Uq(n) Basis

Irreducible represen tations of U_q(m + n) in U_q(m) ⊕ U_q(n) basis are discussed. The noncanonical basis of U_q(m + n) are expanded in terms of its canonical basis. The expansion coefficients or subduction coefficients of U_q (m + n)↓ U_q(m) ⊕ U_q(n) are derived from the subduction coefficients of Hecke algebras.     

Two Types of Infinite-Dimensional Representations of the Quantum Algebra OSPq(l, 4)

In this letter, we discuss the quantum superalgebra OSP_q(l,4). With the help of the SU_q(2)×U(1) basis, we construct two types of representations for the quantum superalgebra, called the-1/2-representation and the 1/2-representation. Both of them are infinitedimensional.     

Cyclic Representation of the q-Deformed Heisenberg-Weyl Superalgebras and the q-Boson-Fermion Realization of Cyclic Represent at ion of Quantum Superalgebra Uqsl(m,n)

A cyclic representation of the q-deformed Heisenberg-Weyl superalgebras is constructed. By making use of this cyclic representation we study the cyclic representations,of quantum superalgebras in terms of their q-boson-fermion realizations with U_qsl(m, n) as an example. Two different q-boson-fermion realizations of U_qsl(m, n) are used and thus two inequivalent cyclic representations of U_qsl(m, n) are obtained.     

经典q变形谐振子及其?量子化

通常所谓的量子包络代数可以在经典Poisson括号的意义下实现,以谐振子系统为例,给出U_q(SU(2))的这种经典实现,指出这种q变形伴随着相空间复坐标的Beltrami变形。并讨论了这种经典q变形谐振子系统的?量子化,得到在Lie括号意义下的U_q(SU(2))代数。 关键词：     

sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

The superalgebra eigenstates (SAES) concept is introduced and then applied to find SAES associated to the sh(2/2) superalgebra, also known as Heisenberg–Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2)Ð sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg–Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the super-Hermitian and -pseudo-super-Hermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.     

q-Fermion and q-Boson Realizations of the Quantum Affine Algebra Uq(sl2) at Roots of Unity

By means of the q-fermion and q-boson rea1ization methods some finite-dimensional irreducible representations of the quantum affine algebra U_q(sl₂), in which the central element is represented as an arbitrary nonzero constant, are explicitly constructed when q is a root of unity.     

U(1/1)q q-Coherent States and Path Integrals for the q-Deformed Jaynes-Cummings Model

The q-coherent states for the quantum superalgebra U(1/1)_q, are introduced. Path integrals in the q-coherent state representations of the U(1/1)_q, are constructed and applied to the q-deformed Jaynes-Cummings model whose dynamical superalgebra is the quantum superalgebra U(1/1)_q.     

R Matrix for UqE7

The quantum Clebsch-Gordan coefficients and the explicit form of the R_q, matrix related with the minimal representation of the quan turn enveloping algebra U_qE₇ are calculated in this paper.     

Jordanian quantum deformations of <Emphasis Type="Italic">D</Emphasis> = 4 anti-de Sitter and Poincaré superalgebras

We consider a superextension of the extended Jordanian twist, describing the non-standard quantization of the anti-de Sitter (AdS) superalgebra in the form of a Hopf superalgebra. The super-Jordanian twisting function and corresponding basic coproduct formulae for the generators of are given in explicit form. A non-linear transformation of the classical superalgebra basis not modifying the defining algebraic relations but simplifying coproducts and antipodes is proposed. Our physical application is in the interpretation of the new super-Jordanian deformation of the superalgebra as deformed D = 4 AdS supersymmetries. Subsequently we perform a suitable contraction of the quantum Jordanian AdS superalgebra and obtain a new -deformation of the D = 4 Poincaré superalgebra, with the bosonic sector describing the light-cone -deformation of the Poincaré symmetries.Received: 19 December 2004, Revised: 13 June 2005, Published online: 19 August 2005     

One-Parameter Indecomposable and Irreducible Representations of gl(2 | 1) Superalgebra

Using inhomogeneous boson–fermion realization, one-parameter indecomposable and irreducible representations of the gl(2 | 1) superalgebra are studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg–weyl superalgebra. All the finite-dimensional irreducible representations of one-parameter of the gl(2 | 1) superalgebra are naturally obtained as special cases. The parameter has relation to the Hubbard interaction parameter U in the Hubbard model for correlated electrons.     

A q-Deformed osp(1,2) Superalgebra and Its Coherent States

In this paper we present a q-deformed osp(1, 2) superalgebra, construct a type of coherent state representations and obtain a q-differential realization for the q-deformed superalgebra.We also study some quantum optical properties of the q-deformed osp(1, 2) coherent states.     

On Two-Parameter Deformations of osp(1|2)(1)

An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra osp(1|2)⁽¹⁾ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of infinite Hopf family of superalgebras, a generalization of the infinite Hopf family of algebras proposed earlier by the authors. The trigonometric and rational degenerations are briefly discussed.     

On charge conjugation

The group of automorphisms of the conformal algebra su(2, 2) has four components giving the usual four components of symmetries of space time. Only two of these components extend to symmetries of the conformal superalgebra — the identity component and the component which induces the parity transformation,P, on space time. There is no automorphism of the conformal superalgebra which inducesT or PT on space time. Automorphisms of su(2, 2) which belong to these last two components induce transformations on the conformal superalgebra which reverse the sign of the odd brackets. In this sense conformal supersymmetry prefers CP to CPT. The operator of charge conjugation acting on spinors, as is found in the standard texts, induces conformal inversion and hence a parity transformation on space time, when considered as acting on the odd generators of the conformal superalgebra. Although it commutes with Lorentz transformations, it does not commute with all of su(2, 2). We propose a different operator for charge conjugation. Geometrically it is induced by the Hodge star operator acting on twistor space. Under the known realization of conformal states from the inclusion SU(2, 2) Sp(8) and the metaplectic representations, its action on states is induced by the unique (up to phase) antilinear intertwining operator between the two metaplectic representations. It is consistent with the split orthosymplectic algebras and hence, by the inclusion of the superconformal in the orthosymplectic, with the orthosymplectic algebra.     

Universal R-matrix of the quantum superalgebra osp(2 | 1)

A quantum analogue of the simplest superalgebra osp(2 | 1) and its finite-dimensional, irreducible representations are found. The corresponding constant solution to the Yang-Baxter equation is constructed and is used to formulate the Hopf superalgebra of functions on the quantum supergroup OSp(2 | 1).     

Supercoherent State and Inhomogeneous Differential Realization of OSP(2, 1) Superalgebra

The supercoherent state of OSP(2, 1) superalgebra is constructed and its propertiesare discussed in detail. The matrix elements of the OSP(2, 1) generators inthe supercoherent state space are calculated. New inhomogeneous differentialrealizations of OSP(2, 1) superalgebra are given.     

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.     

Integrable graded manifolds and nonlinear equations

A method is proposed for the classification of integrable embeddings of (2+2)-dimensional supermanifoldsV _2|2 into an enveloping superspace supplied with the structure of a Lie superalgebra. The approach is first applied to the even part of the scheme, i.e. for the embeddings of 2-dimensional manifoldsV ₂ into Riemannian or non-Riemannian enveloping space. The general consideration is also illustrated by the example of superspaces supplied with the structure of the series sl(n, n+1), whose integrable supermanifolds are described by supersymmetrical 2-dimensional Toda lattice type equations. In particular, forn=1 they are described by the supersymmetrical Liouville and Sine-Gordon equations.     

q-Difference Realization of Uq(sl(M|N)) and Its Application to Free Boson Realization of Uq $$(\widehat{{\text{sl}}}(2|1))$$

We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result, we obtain a free boson realization of the quantum affine superalgebra U_q of an arbitrary level k.