651 research outputs found
On the domain wall partition functions of level-1 affine so(n) vertex models
We derive determinant expressions for domain wall partition functions of
level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing
parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil
The Vertex-Face Correspondence and the Elliptic 6j-symbols
A new formula connecting the elliptic -symbols and the fusion of the
vertex-face intertwining vectors is given. This is based on the identification
of the fusion intertwining vectors with the change of base matrix elements
from Sklyanin's standard base to Rosengren's natural base in the space of even
theta functions of order . The new formula allows us to derive various
properties of the elliptic -symbols, such as the addition formula, the
biorthogonality property, the fusion formula and the Yang-Baxter relation. We
also discuss a connection with the Sklyanin algebra based on the factorised
formula for the -operator.Comment: 23 page
Higher spin vertex models with domain wall boundary conditions
We derive determinant expressions for the partition functions of spin-k/2
vertex models on a finite square lattice with domain wall boundary conditions.Comment: 14 pages, 12 figures. Minor corrections. Version to appear in JSTA
A generalization of the q-Saalschutz sum and the Burge transform
A generalization of the q-(Pfaff)-Saalschutz summation formula is proved.
This implies a generalization of the Burge transform, resulting in an
additional dimension of the ``Burge tree''. Limiting cases of our summation
formula imply the (higher-level) Bailey lemma, provide a new decomposition of
the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc
formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe
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
A class of integrable lattices and KP hierarchy
We introduce a class of integrable -field first-order lattices together
with corresponding Lax equations. These lattices may be represented as
consistency condition for auxiliary linear systems defined on sequences of
formal dressing operators. This construction provides simple way to build
lattice Miura transformations between one-field lattice and -field () ones. We show that the lattices pertained to above class is in some sense
compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge
Integrable theories and loop spaces: fundamentals, applications and new developments
We review our proposal to generalize the standard two-dimensional flatness
construction of Lax-Zakharov-Shabat to relativistic field theories in d+1
dimensions. The fundamentals from the theory of connections on loop spaces are
presented and clarified. These ideas are exposed using mathematical tools
familiar to physicists. We exhibit recent and new results that relate the
locality of the loop space curvature to the diffeomorphism invariance of the
loop space holonomy. These result are used to show that the holonomy is abelian
if the holonomy is diffeomorphism invariant.
These results justify in part and set the limitations of the local
implementations of the approach which has been worked out in the last decade.
We highlight very interesting applications like the construction and the
solution of an integrable four dimensional field theory with Hopf solitons, and
new integrability conditions which generalize BPS equations to systems such as
Skyrme theories. Applications of these ideas leading to new constructions are
implemented in theories that admit volume preserving diffeomorphisms of the
target space as symmetries. Applications to physically relevant systems like
Yang Mills theories are summarized. We also discuss other possibilities that
have not yet been explored.Comment: 64 pages, 8 figure
Differential-difference system related to toroidal Lie algebra
We present a novel differential-difference system in (2+1)-dimensional
space-time (one discrete, two continuum), arisen from the Bogoyavlensky's
(2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity
of the hierarchy, which is related to the vertex operator representation of the
toroidal Lie algebra \sl_2^{tor}.Comment: 10 pages, 4 figures, pLaTeX2e, uses amsmath, amssymb, amsthm,
graphic
On Associativity Equations in Dispersionless Integrable Hierarchies
We discuss the origin of the associativity (WDVV) equations in the context of
quasiclassical or Whitham hierarchies. The associativity equations are shown to
be encoded in the dispersionless limit of the Hirota equations for KP and Toda
hierarchies. We show, therefore, that any tau-function of dispersionless KP or
Toda hierarchy provides a solution to associativity equations. In general, they
depend on infinitely many variables. We also discuss the particular solution to
the dispersionless Toda hierarchy that describes conformal mappings and
construct a family of new solutions to the WDVV equations depending on finite
number of variables.Comment: 16 pages, LaTe
Field of a Radiation Distributuion
General relativistic spherically symmetric matter field with a vanishing
stress energy scalar is analyzed. Procedure for generating exact solutions of
the field equations for such matter distributions is given. It is further
pointed out that all such type I spherically symmetric fields with distinct
eignvalues in the radial two space can be treated as a mixture of isotropic and
directed radiations. Various classes of exact solutions are given. Junction
conditions for such a matter field to the possible exterior solutions are also
discussed.Comment: Latex file, 13 pages, no figures. Accepted for publication in Phys.
Rev.
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