Boson Representations of Subalgebra Chain for Quantum Algebra (Cl)q with q a Root of Unity

The method of q-deformed boson realization is extended to the caee that q is a root of unity. By using thb method, many irreducible and indecomposable representations of each su balgebra in a su balgebra chain of the quantum universal enveloping algebra (quan tum algebra) (C_l)_q are obtained on the q-deformed Fock space and its quotient space. AB an example, the representations of (C₃)_q are constructed in explicit forms. Besides, by embedding (A₁)_q = (C_l)_q, into the subalgebra chain, a new realisation of (A₁)_q and its representations are obtained.     

INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS

The differential realization of Lie superalgebra B(0,1) on the space of inhomogeneous polynomials,and the corresponding inhomogeneous Boson-Fermion realization are studiel.A new kind of indecomposable and irreducible representations of Lie superalgebra B(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra,and on its subspaces and quotient spaces.All the finite dimensional irreducible representations are naturally obtained as special cases.     

Inhomogeneous Inverse Differential Realization of Multimode SU(1, 1) Group

The generators and irreducible representationcoherent state of the multimode SU(1, 1) group inBargmann space are constructed by using the inverseoperators of the multimode bosonic harmonic oscillator, and the inhomogeneous inverse differentialrealization of the multimode SU(1, 1) group arederived.     

The Dyson Realization of the Quantum Group SU(1,1)q and Its Coherent state

The Dyson realization of the quantum group SU(1,1)_q is constructed and the transformation matrix, which turns the Dyson realization into the Holstein Primakoff realization, is given. The coherent state for the Dyson realization is discussed and is found to be the qdeformed Weyl Heisenberg coherent state.     

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：     

Clebsch-Gordan Coefficients for the Two-Parameter Deformed Quantum Algebra SU (1,1)q,s (I)

The Bargmann representations in the tensor product space of the irreducible representations for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the positive discrete series (a) are in trod uced, and the corresponding Bargmann expressions for the bases of irreps, the coherent state and the operators are also derived. The Clebsch-Gordan coefficients (CGC) for the two-parameter deformed quan tum algebra SU(1,1)_q,s corresponding to the positive discrete series (a) are obtained.     

Clebsch-Gordan Coefficients for Two-Parameter Deformed Quantum Algebra SU(1,1)q,s(Ⅱ)

Abstract The Bargmann represen tations in the tensor product space of the irreducible representations for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the negative discrete series (b) are introduced, and the corresponding Bargmann expressions for the bases of irreps, the coherent state and the operators are also derived. The Clebsch-Gordan coeficients (CGC) for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the negative discrete series (b) are obtained.     

Multiboson Realizations of Lie and Quant urn Algebras

A unified method to construct the (multi-)boson realizations of the Lie and quantum algebras is proposed based on a universal deformation of boson (Heisenberg-Weyl) algebra and its multiboson realization. Some explicit examples, the Lie algebras sl(2) and su (Ill), q-boson algebra, quantum algebras sl(2)_q and su (l,l)_q, along with the q-ladder algebra are studied in detail. In particular, the square boson realizations of su (1,l) and su (l,l)_q are naturally obtained as special cases.     

A New q-Deformed Boson Realization of the Quantum Algebra Cq(l) and Its Representations

A new q-deformed boson realization of the quantum algebra C_q(l) is given and some of its finite dimensional representations are explicitly presented when q is a root of unity.     

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.     

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.     

SU(1,1)群的非齐次逆微分实现

利用玻色振子的逆算符构造了SU(1,1)群的生成元和不可约表示的相干态,导出了SU(1,1)群的非齐次逆微分实现.     

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.     

The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

Cyclic Representation of Quantum Group GL(2)q at qp=1 from the Regular Representation of M(2)q1

Regular representation of the matrix element algebra M(2)_q, of the quantum group GL(2)_q is studied, then the cyclic representation of GL(2)_q, is obtained as a quotient module of the regular representation of M(2)_q, with respect to some submodules at q^p = 1.     

Two-Parameter Deformations of SU(2) and SU (1,l) Algebras

The algebras SU(2) and SU(1,1) are promoted to two-parameter quantum universal enveloping algebras (QUEA) by a doubleparameter deformation in this paper. The discrete unitary irreducible representations and their deformed coherent states are studied. The deformed generators are given by a Jordan-Schwinger realization and a Bargmann-Fock representation. It is also interesting that the two-parameter deformed coherent states are found to relate to the oneparameter deformed ones by a simple scaling transformation and this can be used to derive the completeness relation of the former.     

Inhomogeneous inverse differential realization of multimodeSU(2) group

The generators and irreducible representation coherent state of the multimodeSU(2) group are constructed by using the inverse operators of the multimode bosonic harmonic oscillator, and the inhomogeneous inverse differential realization of the multimodeSU(2) group are derived.     

Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, R_νλ (ν, λ=0, ±1), are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of R_νλ are given. The expectation values of R_νλ in the angular momentum coherent states are calculated as well as the corresponding classical limits.     

Simple Coherent State and New Form for Inhomogeneous Differential Realization of OSP(2,1) Superalgebra

The simple coherent state of the OSP(2,1) superalgebra is constructed and its properties are discussed in detail. The matrix elements of the OSP(2,1) generators in the coherent state space are calculated. The new form for inhomogeneous differential realization of the OSP(2,1) superalgebra is given.