N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su（1,1）. The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp（1,2） or B（0,1） in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

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.     

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：     

Inhomogeneous q-Differential Realization,Inhomogeneous q-Boson Realization of Quantum Group SU(n)q and Its Indecomposable Representations

An inhomogeneous q-differential realization (q-IHDR) and its corresponding inhomogeneous q-boson realization (q-IHBR) of quantum group SU(n)_q are studied. By making use of the q-IHBR a kind of infinite dimensional indecomposable and irreducible representations of SU(n)_q is studied on the q-Fcck space. The finite dimensional irreducible representations of SU(n), are obtained on the finite dimensional subspaces of q-Fock space. As an example, these representations of SU(2)_q are studied in detail and Jimbo standard irreducible representations are obtained.     

Infinite-Dimensional Lie Superalgebras and Hook Schur Functions

 Making use of a Howe duality involving the infinite-dimensional Lie superalgebra and the finite-dimensional group GL _l of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of in terms of hook Schur functions. We use the reduction procedure of to to derive a character formula for a certain class of level 1 highest weight irreducible representations of, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra . These modules turn out to form the complete set of integrable -modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible -modules may be written as a sum of products of hook Schur functions. Received: 6 March 2002 / Accepted: 15 January 2003 Published online: 14 March 2003 RID="*" ID="*" Partially supported by NSC-grant 91-2115-M-002-007 of the R.O.C. RID="**" ID="**" Partially supported by NSC-grant 90-2115-M-006-015 of the R.O.C. Communicated by M. Aizenman     

Classification of irreducible super-unitary representations ofsu(p,q/n)

In this paper we classify all the irreducible super-unitary representations ofsu(p,q/n), which can be integrated up to a unitary representation ofS(U(p,q)×U(n)), a Lie group corresponding to the even part ofsu(p,q/n). Note that a real form of the Lie superalgebrasl(m/n;) which has non-trivial superunitary representations is of the formsu(p,q/n)(p+q=m) orsu(m/r,s)(r+s=n). Moreover, we give an explicit realization for each irreducible super-unitary representation, using the oscillator representation of an orthosymplectic Lie superalgebra.     

Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK 6

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK ₆, for which E(1, 6) is the annihilation superalgebra.     

Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function

We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this construction shows, in particular, that in the simplest case of the sℓ (2|1) level 1 affine superalgebra the characters are expressed in terms of the Appell elliptic function. Our results demonstrate that the representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras. Received: 17 April 2000 / Accepted: 7 July 2000     

The gl (M|N) super Yangian and its finite-dimensional representations

Methods are developed for systematically constructing the finite-dimensional irreducible representations of the super Yangian Y (gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite-dimensional irreducible representation of Y (gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite-dimensional are given.     

Gelfand–Tsetlin Pattern and Strict Partitions

We give a representation-theoretical interpretation of the Gelfand–Tsetlin pattern for strict partitions. Using the Howe duality involving a pair of the queer Lie superalgebras and an analogue of the Littlewood–Richardson rule for Schur Q-functions, we show that such patterns give the branching rule for the irreducible tensor representations of the queer Lie superalgebra.     

Cyclic Representations of Quantum (Super) Algebras At qp=1

Cyclic representations of quantum (super) algebras are studied at q^p=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra U_qosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras.     

Parabosons,parafermions, and explicit representations of infinite-dimensional algebras

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(∞) and of the Lie superalgebra osp(1|∞). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.     

Group-Theoretical Approach to Extended Conformal Supersymmetry: Function Space Realizations and Invariant Differential Operators

We give function space realizations of all representations of the conformal superalgebra su(2,2/N) and of the supergroup SU(2, 2 /N) induced from irreducible finite-dimensional Lorentz and SU(N) representations realized without spin and isospin indices. We use the lowest weight module structure of our su(2,2/N) representations to present a general procedure (adapted from the semisimple Lie algebra case) for the canonical construction of invariant differential operators closely related to the reducible (indecomposable) representations. All conformal supercovariant derivatives are obtained in this way. Examples of higher order invariant differential operators are given.     

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).     

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...     

Coherent states and induced representations

A generalization of the notion of coherent states is given. The following one-to-one correspondences are pointed out: (1) between covariant overcomplete systems of coherent states and a class of covariant semi-spectral measures; (2) between covariant semispectral measures and unitary irreducible subrepresentations of induced representations of Lie groups; (3) between unitary irreducible representations of Lie groups with covariant overcomplete systems of coherent states and unitary irreducible subrepresentations of induced representations, whose representation spaces are reproducing kernel Hilbert spaces.     

The cyclic representations of the quantum superalgebra U q osp(2, 1) withq a root of unity

By generalizing De Concini and Kac's cyclic representation theory of quantum groups at roots of unity, the cyclic representations of the quantum superalgebra U _q osp(2, 1) are constructed in three classes: irreducible representations with single multiplicities, irreducible representations with the multiplicities larger than one, and indecomposable representations.This work is supported in part by the National Sciene Foundation in China.