1,534 research outputs found
Extended T-systems
We use the theory of q-characters to establish a number of short exact
sequences in the category of finite-dimensional representations of the quantum
affine groups of types A and B. That allows us to introduce a set of 3-term
recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic
On multigraded generalizations of Kirillov-Reshetikhin modules
We study the category of Z^l-graded modules with finite-dimensional graded
pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre
subcategories with finitely many isomorphism classes of simple objects. We
construct projective resolutions for the simple modules in these categories and
compute the Ext groups between simple modules. We show that the projective
covers of the simple modules in these Serre subcategories can be regarded as
multigraded generalizations of Kirillov-Reshetikhin modules and give a
recursive formula for computing their graded characters
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
Let Uq(ghat) be the quantum affine algebra associated to a simply-laced
simple Lie algebra g. We examine the relationship between Dorey's rule, which
is a geometrical statement about Coxeter orbits of g-weights, and the structure
of q-characters of fundamental representations V_{i,a} of Uq(ghat). In
particular, we prove, without recourse to the ADE classification, that the rule
provides a necessary and sufficient condition for the monomial 1 to appear in
the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical
Physic
New concept of relativistic invariance in NC space-time: twisted Poincar\'e symmetry and its implications
We present a systematic framework for noncommutative (NC) QFT within the new
concept of relativistic invariance based on the notion of twisted Poincar\'e
symmetry (with all 10 generators), as proposed in ref. [7]. This allows to
formulate and investigate all fundamental issues of relativistic QFT and offers
a firm frame for the classification of particles according to the
representation theory of the twisted Poincar\'e symmetry and as a result for
the NC versions of CPT and spin-statistics theorems, among others, discussed
earlier in the literature. As a further application of this new concept of
relativism we prove the NC analog of Haag's theorem.Comment: 15 page
q-Deformed de Sitter/Conformal Field Theory Correspondence
Unitary principal series representations of the conformal group appear in the
dS/CFT correspondence. These are infinite dimensional irreducible
representations, without highest weights. In earlier work of Guijosa and the
author it was shown for the case of two-dimensional de Sitter, there was a
natural q-deformation of the conformal group, with q a root of unity, where the
unitary principal series representations become finite-dimensional cyclic
unitary representations. Formulating a version of the dS/CFT correspondence
using these representations can lead to a description with a finite-dimensional
Hilbert space and unitary evolution. In the present work, we generalize to the
case of quantum-deformed three-dimensional de Sitter spacetime and compute the
entanglement entropy of a quantum field across the cosmological horizon.Comment: 18 pages, 2 figures, revtex, (v2 reference added
Effect of quantum group invariance on trapped Fermi gases
We study the properties of a thermodynamic system having the symmetry of a
quantum group and interacting with a harmonic potential. We calculate the
dependence of the chemical potential, heat capacity and spatial distribution of
the gas on the quantum group parameter and the number of spatial dimensions
. In addition, we consider a fourth-order interaction in the quantum group
fields , and calculate the ground state energy up to first order.Comment: LaTeX file, 20 pages, four figures, uses epsf.sty, packaged as a
single tar.gz uuencoded fil
Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
This paper completes a series devoted to explicit constructions of
finite-dimensional irreducible representations of the classical Lie algebras.
Here the case of odd orthogonal Lie algebras (of type B) is considered (two
previous papers dealt with C and D types). A weight basis for each
representation of the Lie algebra o(2n+1) is constructed. The basis vectors are
parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the
matrix elements of generators of o(2n+1) in this basis are given. The
construction is based on the representation theory of the Yangians. A similar
approach is applied to the A type case where the well-known formulas due to
Gelfand and Tsetlin are reproduced.Comment: 29 pages, Late
The staggered vertex model and its applications
New solvable vertex models can be easily obtained by staggering the spectral
parameter in already known ones. This simple construction reveals some
surprises: for appropriate values of the staggering, highly non-trivial
continuum limits can be obtained. The simplest case of staggering with period
two (the case) for the six-vertex model was shown to be related, in one
regime of the spectral parameter, to the critical antiferromagnetic Potts model
on the square lattice, and has a non-compact continuum limit. Here, we study
the other regime: in the very anisotropic limit, it can be viewed as a zig-zag
spin chain with spin anisotropy, or as an anyonic chain with a generic
(non-integer) number of species. From the Bethe-Ansatz solution, we obtain the
central charge , the conformal spectrum, and the continuum partition
function, corresponding to one free boson and two Majorana fermions. Finally,
we obtain a massive integrable deformation of the model on the lattice.
Interestingly, its scattering theory is a massive version of the one for the
flow between minimal models. The corresponding field theory is argued to be a
complex version of the Toda theory.Comment: 38 pages, 14 figures, 3 appendice
New integrable extension of the Hubbard chain with variable range hopping
New integrable variant of the one-dimensional Hubbard model with
variable-range correlated hopping is studied. The Hamiltonian is constructed by
applying the quantum inverse scattering method on the infinite interval at zero
density to the one-parameter deformation of the L-matrix of the Hubbard model.
By construction, this model has Y(su(2))Y(su(2)) symmetry in the
infinite chain limit. Multiparticle eigenstates of the model are investigated
through this method.Comment: 25 pages, LaTeX, no figure
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