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.     

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.     

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.     

Quantum Deformation of the Lie Superalgebra spl(2, 1)

In this paper we obtain a q-deformation of theLie superalgebra spl(2, 1), which is in correspondencewith its one-parameter quantum group. This proceduresuggests a two-parameter deformation of the Lie superalgebra which leads to the two-parameterquantum group.     

Quantum Group Structure of Lie Superalgebra osp (1/2)

We quantize the enveloping Lie superalgebraU(osp(1/2)) in the nonstandard simple root system withtwo odd simple roots. The quantum supergroup structureassociated with the nonstandard simple root system is also given.     

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.     

Differential Operator Realization of the Exceptional Superalgebra D(2,1;α) and Its Application

In this paper, we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α). Based on these expressions, we construct free field realizations of the currents associated with D(2,1;α) at an arbitrary level k.     

Extensions of the Neveu–Schwarz Lie Superalgebra

We consider the generalizations of the Virasoro Lie algebra constructed recently in [16] and we classify their superanalogues. The main result of this article is a series of Lie Superalgebras generalizing the well-known Neveu–Schwarz Superalgebra. Received: 26 May 1998 / Accepted: 8 April 1999     

Equivalence of Blocks for the General Linear Lie Superalgebra

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category ${\mathcal{O}}$ for a general linear Lie superalgebra to an integral block of ${\mathcal{O}}$ for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of ${\mathcal{O}}$ .     

An Analogue of Holstein-Primakoff and Dyson Realizations for Lie Superalgebras. The Lie Superalgebra sl(1/n)

Abstract

An analogue of the Holstein-Primakoff and Dyson realizations for the Lie superalgebra sl(1/n) is written down. Expressions are the same as for the Lie algebra sl(n + 1), however in the latter, Bose operators have to be replaced with Fermi operators.     

Deforming the Lie Superalgebra of Contact Vector Fields on S1|1 Inside the Lie Superalgebra of Superpseudodifferential Operators on S1|1

Abstract

We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie superalgebra of superpseudodifferential operators on the supercircle. This approach leads to the deformations of the central charge induced on K(1) by the canonical central extension of SΨDO.     

Representation Theory of the Affine Lie Superalgebra at Fractional Level

N= 2 noncritical strings are closely related to the Wess-Zumino-Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the precise knowledge of the representation theory at fractional level. In this paper, the embedding diagrams of singular vectors appearing in Verma modules for fractional values of the level (, p and q coprime) are derived analytically. The nilpotency of the fermionic generators in $\hslc$ requires the introduction of a nontrivial generalisation of the MFF construction to relate singular vectors among themselves. The diagrams reveal a striking similarity with the degenerate representations of the N= 2 superconformal algebra. Received: 10 June 1996\,/\,Accepted: 8 October 1996     

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     

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.