135 research outputs found
Gel'fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor
representations of the Lie superalgebra gl(m|n). Explicit expressions for the
generators of the Lie superalgebra acting on this basis are determined.
Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of
any covariant tensor representation of gl(m|n) with the natural representation
V ([1,0,...,0]) of gl(m|n) with highest weight (1,0,. . . ,0) are computed.
Both results are steps for the explicit construction of the parastatistics Fock
space.Comment: 16 page
Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]
Tensor operators in graded representations of Z_{2}-graded Hopf algebras are
defined and their elementary properties are derived. Wigner-Eckart theorem for
irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of
tensor operators in the irreducible representation space of Hopf algebra
U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the
irreducible tensor operators are calculated. A construction of some elements of
the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late
Comments on Drinfeld Realization of Quantum Affine Superalgebra and its Hopf Algebra Structure
By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to
supersymmetric cases, we obtain Drinfeld current realization for quantum affine
superalgebra . We find a simple coproduct for the quantum
current generators and establish the Hopf algebra structure of this super
current algebra.Comment: Some errors and misprints corrected and a remark in section 4
removed. 12 pages, Latex fil
Lattice Models
In this paper I construct lattice models with an underlying
superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation.
These {\it trigonometric} -matrices depend on {\it three} continuous
parameters, the spectral parameter, the deformation parameter and the
parameter, , of the superalgebra. It must be emphasized that the
parameter is generic and the parameter does not correspond to the
`nilpotency' parameter of \cite{gs}. The rational limits are given; they also
depend on the parameter and this dependence cannot be rescaled away. I
give the Bethe ansatz solution of the lattice models built from some of these
-matrices, while for other matrices, due to the particular nature of the
representation theory of , I conjecture the result. The parameter
appears as a continuous generalized spin. Finally I briefly discuss the problem
of finding the ground state of these models.Comment: 19 pages, plain LaTeX, no figures. Minor changes (version accepted
for publication
Finite dimensional representations of at arbitrary
A method is developed to construct irreducible representations(irreps) of the
quantum supergroup in a systematic fashion. It is shown that
every finite dimensional irrep of this quantum supergroup at generic is a
deformation of a finite dimensional irrep of its underlying Lie superalgebra
, and is essentially uniquely characterized by a highest weight. The
character of the irrep is given. When is a root of unity, all irreps of
are finite dimensional; multiply atypical highest weight irreps
and (semi)cyclic irreps also exist. As examples, all the highest weight and
(semi)cyclic irreps of are thoroughly studied.Comment: 21 page
Wigner quantum oscillators. Osp(3/2) oscillators
The properties of the three-dimensional noncanonical osp(3/2) oscillators,
introduced in J.Phys. A: Math. Gen. {\bf 27} (1994) 977, are further studied.
The angular momentum M of the oscillators can take at most three values
M=p-1,p,p+1, which are either all integers or all half-integers. The
coordinates anticommute with each other. Depending on the state space the
energy spectrum can coincide or can be essentially different from those of the
canonical oscillator. The ground state is in general degenerated.Comment: TeX, Preprint INRNE-TH-94/3, 17
Conserved Charges in the Principal Chiral Model on a Supergroup
The classical principal chiral model in 1+1 dimensions with target space a
compact Lie supergroup is investigated. It is shown how to construct a local
conserved charge given an invariant tensor of the Lie superalgebra. We
calculate the super-Poisson brackets of these currents and argue that they are
finitely generated. We show how to derive an infinite number of local charges
in involution. We demonstrate that these charges Poisson commute with the
non-local charges of the model
On representations of super coalgebras
The general structure of the representation theory of a -graded
coalgebra is discussed. The result contains the structure of Fourier analysis
on compact supergroups and quantisations thereof as a special case. The general
linear supergroups serve as an explicit illustration and the simplest example
is carried out in detail.Comment: 18 pages, LaTeX, KCL-TH-94-
Hom-Lie color algebra structures
This paper introduces the notion of Hom-Lie color algebra, which is a natural
general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include
also as special cases Lie (super) algebras and Lie color algebras. We study the
homomorphism relation of Hom-Lie color algebras, and construct new algebras of
such kind by a \sigma-twist. Hom-Lie color admissible algebras are also defined
and investigated. They are finally classified via G-Hom-associative color
algebras, where G is a subgroup of the symmetric group S_3.Comment: 16 page
Exact exponents for the spin quantum Hall transition
We consider the spin quantum Hall transition which may occur in disordered
superconductors with unbroken SU(2) spin-rotation symmetry but broken
time-reversal symmetry. Using supersymmetry, we map a model for this transition
onto the two-dimensional percolation problem. The anisotropic limit is an
sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical
exponents associated with disorder-averages of several observables in good
agreement with recent numerical results.Comment: 5 pages, 2 figure
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