The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

Dose-Related Effects of ACE Inhibition in Man: Quinapril in Patients with Moderate Congestive Heart Failure

Early treatment with ACE inhibitors of even moderate heart failure is clinically beneficial, even though haemodynamic measurements cannot adequately quantitate such improvement. Neurohumoral assessment is, however, supposed to be more accurate In 55 patients with moderate heart failure (ejection fraction ≤ 35%), we investigated the dose-dependent effects of ACE inhibition with quinapril taken orally (2.5, 5 or 10 mg b.i.d.) following a placebo-controlled, parallel design protocol over 12 weeks. Plasma components of the renin angiotensin system, catecholamines and ANF were measured together with haemodymmics both at rest and during exercise. Before ACE inhibitor treatment, median PRA, Ang I and II and catecholamines were normal, while ANF was increased All these parameters including ACE activity, rose during exercise. Chronic inhibition of ACE activity was dose-dependent and the maximal fall in Ang If occurred with quinapril 20 mg.day−1. Humoral changes appeared more assessible than haemodymmic alterations even though many of these changes were reasonably correlated. The effects of chronic ACE inhibition on circulating neurohumoral components in patients with moderate heart failure are small and dose-dependent. Since humoral changes are related to haemodynamics they should account for the clinical benefit. Appropriately high doses of ACE inhibitors should be chosen for treatment of heart failur

Boundary breathers in the sinh-Gordon model

We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary conditions which preserve the \phi --> -\phi symmetry of the bulk theory, the energy spectrum of the boundary states is computed in two ways: firstly, by using the bootstrap technique and subsequently, by using a WKB approximation. Requiring that the two descriptions of the spectrum agree with each other allows a determination of the relationship between the boundary parameter, the bulk coupling constant, and the parameter appearing in the reflection factor derived by Ghoshal to describe the scattering of the sinh-Gordon particle from the boundary.Comment: 16 pages amslate

Reflection equation for the N=3 Cremmer-Gervais R-matrix

We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety $\mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$ and $\mathbb{C} \times \mathbb{P}^1(\mathbb{C}) \times \mathbb{P}^2(\mathbb{C})$.Comment: 28 pages, revised versio

On Quantum Lie Algebras and Quantum Root Systems

As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum Lie bracket given by the quantum adjoint action. The structure constants of these algebras depend on the quantum deformation parameter $q$ and they go over into the usual Lie algebras when $q=1$. The notions of q-conjugation and q-linearity are introduced. q-linear analogues of the classical antipode and Cartan involution are defined and a generalised Killing form, q-linear in the first entry and linear in the second, is obtained. These structures allow the derivation of symmetries between the structure constants of quantum Lie algebras. The explicitly worked out examples of $g=sl_3$ and $so_5$ illustrate the results.Comment: 22 pages, latex, version to appear in J. Phys. A. see http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further informatio

Quantum affine Toda solitons

We review some of the progress in affine Toda field theories in recent years, explain why known dualities cannot easily be extended, and make some suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision

Eight state supersymmetric UU model of strongly correlated fermions

An integrable eight state supersymmtric $U$ model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has an $gl(3|1)$ supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained.Comment: Some cosmetic changes; to appear in Phys. Rev.