1,113 research outputs found
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
Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)
We investigate a one-parameter family of quantum Harish-Chandra modules of
U_q sl(2n). This family is an analog of the holomorphic discrete series of
representations of the group SU(n,n) for the quantum group U_q su(n, n). We
introduce a q-analog of "the wave" operator (a determinant-type differential
operator) and prove certain covariance property of its powers. This result is
applied to the study of some quotients of the above-mentioned quantum
Harish-Chandra modules. We also prove an analog of a known result by J.Faraut
and A.Koranyi on the expansion of reproducing kernels which determines the
analytic continuation of the holomorphic discrete series.Comment: 26 page
Remarks on the multi-species exclusion process with reflective boundaries
We investigate one of the simplest multi-species generalizations of the one
dimensional exclusion process with reflective boundaries. The Markov matrix
governing the dynamics of the system splits into blocks (sectors) specified by
the number of particles of each kind. We find matrices connecting the blocks in
a matrix product form. The procedure (generalized matrix ansatz) to verify that
a matrix intertwines blocks of the Markov matrix was introduced in the periodic
boundary condition, which starts with a local relation [Arita et al, J. Phys. A
44, 335004 (2011)]. The solution to this relation for the reflective boundary
condition is much simpler than that for the periodic boundary condition
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
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
Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
We connect two alternative concepts of solving integrable models, Baxter's
method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz.
The main steps of the calculation are performed in a general setting and a
formula for the Bethe eigenvalues of the Q-operator is derived. A proof is
given for states which contain up to three Bethe roots. Further evidence is
provided by relating the findings to the six-vertex fusion hierarchy. For the
XXZ spin-chain we analyze the cases when the deformation parameter of the
underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page
On the Two q-Analogue Logarithmic Functions
There is a simple, multi-sheet Riemann surface associated with e_q(z)'s
inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be
defined. However, the topology of the Riemann surface for ln_q(w) changes each
time "q" increases above the collision point of a pair of the turning points of
e_q(x). There is also a power series representation for ln_q(1+w). An
infinite-product representation for e_q(z) is used to obtain the ordinary
natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of
e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power
series in terms of values of these sum rules. The values of the sum rules for
the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the
usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General.
Some explict formulas added, and to update the reference
The quantum superalgebra : deformed para-Bose operators and root of unity representations
We recall the relation between the Lie superalgebra and para-Bose
operators. The quantum superalgebra , defined as usual in terms
of its Chevalley generators, is shown to be isomorphic to an associative
algebra generated by so-called pre-oscillator operators satisfying a number of
relations. From these relations, and the analogue with the non-deformed case,
one can interpret these pre-oscillator operators as deformed para-Bose
operators. Some consequences for (Cartan-Weyl basis,
Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra are
pointed out. Finally, using a realization in terms of ``-commuting''
-bosons, we construct an irreducible finite-dimensional unitary Fock
representation of and its decomposition in terms of
representations when is a root of unity.Comment: 15 pages, LaTeX (latex twice), no figure
Neutralizing antibodies against West Nile virus identified directly from human B cells by single-cell analysis and next generation sequencing
West Nile virus (WNV) infection is an emerging mosquito-borne disease that can lead to severe neurological illness and currently has no available treatment or vaccine. Using microengraving, an integrated single-cell analysis method, we analyzed a cohort of subjects infected with WNV - recently infected and post-convalescent subjects - and efficiently identified four novel WNV neutralizing antibodies. We also assessed the humoral response to WNV on a single-cell and repertoire level by integrating next generation sequencing (NGS) into our analysis. The results from single-cell analysis indicate persistence of WNV-specific memory B cells and antibody-secreting cells in post-convalescent subjects. These cells exhibited class-switched antibody isotypes. Furthermore, the results suggest that the antibody response itself does not predict the clinical severity of the disease (asymptomatic or symptomatic). Using the nucleotide coding sequences for WNV-specific antibodies derived from single cells, we revealed the ontogeny of expanded WNV-specific clones in the repertoires of recently infected subjects through NGS and bioinformatic analysis. This analysis also indicated that the humoral response to WNV did not depend on an anamnestic response, due to an unlikely previous exposure to the virus. The innovative and integrative approach presented here to analyze the evolution of neutralizing antibodies from natural infection on a single-cell and repertoire level can also be applied to vaccine studies, and could potentially aid the development of therapeutic antibodies and our basic understanding of other infectious diseases
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