248 research outputs found
On Casimir's Ghost
We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard
adjoint action, endowing it with a module structure. This allows, in
particular, to construct a bosonic operator which anticommutes with all the
fermionic generators and which appears to be the square root of a certain
Casimir operator.Comment: LaTeX2e, 13 pages,also available at
http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP587.ps.gz ; one sentence removed
and a note added. Not a major revisio
Atypical Representations of at Roots of Unity
We show how to adapt the Gelfand-Zetlin basis for describing the atypical
representation of when is root of
unity. The explicit construction of atypical representation is presented in
details for .Comment: 18 pages, Tex-file and 2 figures. Uuencoded, compressed and tared
archive of plain tex file and postscript figure file. Upon uudecoding,
uncompressing and taring, tex the file atypique.te
Finite Chains with Quantum Affine Symmetries
We consider an extension of the (t-U) Hubbard model taking into account new
interactions between the numbers of up and down electrons. We confine ourselves
to a one-dimensional open chain with L sites (4^L states) and derive the
effective Hamiltonian in the strong repulsion (large U) regime. This
Hamiltonian acts on 3^L states. We show that the spectrum of the latter
Hamiltonian (not the degeneracies) coincides with the spectrum of the
anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L
states). The wave functions of the 3^L-state system are obtained explicitly
from those of the 2^L-state system, and the degeneracies can be understood in
terms of irreducible representations of U_q(\hat{sl(2)}).Comment: 31pp, Latex, CERN-TH.6935/93. To app. in Int. Jour. Mod. Phys. A.
(The title of the paper is changed. This is the ONLY change. Previous title
was: Hubbard-Like Models in the Infinite Repulsion Limit and
Finite-Dimensional Representations of the Affine Algebra U_q(\hat{sl(2)}).
On the Quasi-Hopf structure of deformed double Yangians
We construct universal twists connecting the centrally extended double
Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby
establishing the quasi-Hopf structures of the latter.Comment: 11 page
Integrable XYZ Model with Staggered Anisotropy Parameter
We apply to the XYZ model the technique of construction of integrable models
with staggered parameters, presented recently for the XXZ case. The solution of
modified Yang-Baxter equations is found and the corresponding integrable
zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ
case in the appropriate limit.Comment: 8 pages ; epic packag
Deformed Double Yangian Structures
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N))
are defined for any N, extending the previously known case of N=2. They realise
deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the
quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras
A_qp(sl(N)), these algebras contain subalgebras at critical values of the
central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when
c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations
are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra
Composition of Kinetic Momenta: The U_q(sl(2)) case
The tensor products of (restricted and unrestricted) finite dimensional
irreducible representations of \uq are considered for a root of unity.
They are decomposed into direct sums of irreducible and/or indecomposable
representations.Comment: 27 pages, harvmac and tables macros needed, minor TeXnical revision
to allow automatic TeXin
Representations of U_q(sl(N)) at Roots of Unity
The Gelfand--Zetlin basis for representations of is improved to
fit better the case when is a root of unity. The usual -deformed
representations, as well as the nilpotent, periodic (cyclic), semi-periodic
(semi-cyclic) and also some atypical representations are now described with the
same formalism.Comment: 18 pages, Plain TeX, Macros harvmac.tex and epsf needed 3 figures in
a uuencoded tar separate file. Some references are added. Also available at
http://lapphp0.in2p3.fr/preplapp/psth/uqsln.ps.g
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