230 research outputs found
Scattering matrices and affine Hecke algebras
We construct the scattering matrices for an arbitrary Weyl group in terms of
elementary operators which obey the generalised Yang-Baxter equation. We use
this construction to obtain the affine Hecke algebras. The center of the affine
Hecke algebras coincides with commuting Hamiltonians. These Hamiltonians have
q-deformed affine Lie algebras as symmetry algebra.Comment: 22 pages, harvmac, no figures, Lecture at Schladming, March 4,11 199
Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation
The sine-Gordon equation is considered in the hamiltonian framework provided
by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional
coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is
parametrized by a finite dimensional symplectic vector space embedded into
\grg^* by a moment map. Real quasiperiodic solutions are computed in terms of
theta functions using a Liouville generating function which generates a
canonical transformation to linear coordinates on the Jacobi variety of a
suitable hyperelliptic curve.Comment: 12 pg
The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra
We decompose the level-1 irreducible highest weight modules of the quantum
affine algebra with respect to the level-0 --action defined in q-alg/9702024. The decomposition is
parameterized by the skew Young diagrams of the border strip type.Comment: 22 pages, AMSLaTe
Completely splittable representations of affine Hecke-Clifford algebras
We classify and construct irreducible completely splittable representations
of affine and finite Hecke-Clifford algebras over an algebraically closed field
of characteristic not equal to 2.Comment: 39 pages, v2, added a new reference with comments in section 4.4,
added two examples (Example 5.4 and Example 5.11) in section 5, mild
corrections of some typos, to appear in J. Algebraic Combinatoric
Algebraic Structures of Quantum Projective Field Theory Related to Fusion and Braiding. Hidden Additive Weight
The interaction of various algebraic structures describing fusion, braiding
and group symmetries in quantum projective field theory is an object of an
investigation in the paper. Structures of projective Zamolodchikov al- gebras,
their represntations, spherical correlation functions, correlation characters
and envelopping QPFT-operator algebras, projective \"W-algebras, shift
algebras, braiding admissible QPFT-operator algebras and projective
G-hypermultiplets are explored. It is proved (in the formalism of shift
algebras) that sl(2,C)-primary fields are characterized by their projective
weights and by the hidden additive weight, a hidden quantum number discovered
in the paper (some discussions on this fact and its possible relation to a
hidden 4-dimensional QFT maybe found in the note by S.Bychkov, S.Plotnikov and
D.Juriev, Uspekhi Matem. Nauk 47(3) (1992)[in Russian]). The special attention
is paid to various constructions of projective G-hyper- multiplets
(QPFT-operator algebras with G-symmetries).Comment: AMS-TEX, amsppt style, 16 pages, accepted for a publication in
J.MATH.PHYS. (Typographical errors are excluded
Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
We show that a suitable coset algebra, constructed in terms of an extension
of the Zamolodchikov-Faddeev algebra, is homomorphic to the
Reflection-Transmission algebra, as it appears in the study of integrable
systems with impurity.Comment: 8 pages; a misprint in eq. (2.14) and (2.15) has been correcte
Bethe Equations for a g_2 Model
We prove, using the coordinate Bethe ansatz, the exact solvability of a model
of three particles whose point-like interactions are determined by the root
system of g_2. The statistics of the wavefunction are left unspecified. Using
the properties of the Weyl group, we are also able to find Bethe equations. It
is notable that the method relies on a certain generalized version of the
well-known Yang-Baxter equation. A particular class of non-trivial solutions to
this equation emerges naturally.Comment: 10 pages, 3 figure
Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
In this proceeding we present the nested Bethe ansatz for open spin chains of
XXX-type, with arbitrary representations (i.e. `spins') on each site of the
chain and diagonal boundary matrices . The nested Bethe anstaz
applies for a general , but a particular form of the matrix.
We give the eigenvalues, Bethe equations and the form of the Bethe vectors for
the corresponding models. The Bethe vectors are expressed using a trace
formula.Comment: 15 pages, proceeding for Dubna International SQS 09 Worksho
Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models
In this paper we compute the most general nondiagonal reflection matrices of
the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter
equations. We find new one-parameter family of reflection matrices for the RSOS
model in addition to the previous result without any parameter. We also find
three classes of reflection matrices for the SOS model, which has one or two
parameters. For the hard hexagon model which can be mapped to RSOS(5) model by
folding four RSOS heights into two, the solutions can be obtained similarly
with a main difference in the boundary unitarity conditions. Due to this, the
reflection matrices can have two free parameters. We show that these extra
terms can be identified with the `decorated' solutions. We also generalize the
hard hexagon model by `folding' the RSOS heights of the general RSOS(p) model
and show that they satisfy the integrability conditions such as the Yang-
Baxter and boundary Yang-Baxter equations. These models can be solved using the
results for the RSOS models.Comment: 18pages,Late
Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to .Comment: 6 page
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