268 research outputs found
Integrable open boundary conditions for XXC models
The XXC models are multistate generalizations of the well known spin 1/2 XXZ
model. These integrable models share a common underlying su(2) structure. We
derive integrable open boundary conditions for the hierarchy of conserved
quantities of the XXC models . Due to lack of crossing unitarity of the
R-matrix, we develop specific methods to prove integrability. The symmetry of
the spectrum is determined.Comment: Latex2e, 10 page
On the R-matrix realization of Yangians and their representations
We study the Yangians Y(a) associated with the simple Lie algebras a of type
B, C or D. The algebra Y(a) can be regarded as a quotient of the extended
Yangian X(a) whose defining relations are written in an R-matrix form. In this
paper we are concerned with the algebraic structure and representations of the
algebra X(a). We prove an analog of the Poincare-Birkhoff-Witt theorem for X(a)
and show that the Yangian Y(a) can be realized as a subalgebra of X(a).
Furthermore, we give an independent proof of the classification theorem for the
finite-dimensional irreducible representations of X(a) which implies the
corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit
constructions for all fundamental representation of the Yangians.Comment: 65 page
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
Generalization of the U_q(gl(N)) algebra and staggered models
We develop a technique of construction of integrable models with a Z_2
grading of both the auxiliary (chain) and quantum (time) spaces. These models
have a staggered disposition of the anisotropy parameter. The corresponding
Yang-Baxter Equations are written down and their solution for the gl(N) case
are found. We analyze in details the N=2 case and find the corresponding
quantum group behind this solution. It can be regarded as quantum
U_{q,B}(gl(2)) group with a matrix deformation parameter qB with (qB)^2=q^2.
The symmetry behind these models can also be interpreted as the tensor product
of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator
related to deformation parameter -1.Comment: 12 pages ; Latex2
Covariant un-reduction for curve matching
The process of un-reduction, a sort of reversal of reduction by the Lie group
symmetries of a variational problem, is explored in the setting of field
theories. This process is applied to the problem of curve matching in the
plane, when the curves depend on more than one independent variable. This
situation occurs in a variety of instances such as matching of surfaces or
comparison of evolution between species. A discussion of the appropriate
Lagrangian involved in the variational principle is given, as well as some
initial numerical investigations.Comment: Conference paper for MFCA201
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