A Free Field Representation of the Screening Currents of $U_q(\widehat{sl(3)})

We construct five independent screening currents associated with the $U_q(\widehat{sl(3)})$ quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the quantum analogue of the Wakimoto realization of the current algebra. Four of the screening currents are `simple', in that each one is given as a single exponential field. The fifth is expressed as an infinite sum of exponential fields. For reasons we discuss, we expect that the structure of the screening currents for a general quantum affine algebra will be similar to the $U_q(\widehat{sl(3)})$ case.Comment: 21 pages (LaTeX), CRM-126

The Dynamical Correlation Function of the XXZ Model

We perform a spectral decomposition of the dynamical correlation function of the spin $1/2$ XXZ model into an infinite sum of products of form factors. Beneath the four-particle threshold in momentum space the only non-zero contributions to this sum are the two-particle term and the trivial vacuum term. We calculate the two-particle term by making use of the integral expressions for form factors provided recently by the Kyoto school. We evaluate the necessary integrals by expanding to twelfth order in $q$. We show plots of $S(w,k)$, for $k=0$ and $\pi$ at various values of the anisotropy parameter, and for fixed anisotropy at various $k$ around $0$ and $\pi$.Comment: 20 pages (LaTeX), CRM-219

Vertex Operators and Matrix Elements of Uq(su(2)k)U_q(su(2)_k) via Bosonization

We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2)_k)$ for arbitrary level $k$ and representation $j\leq k/2$. Both are obtained directly as two solutions of the defining condition of vertex operators - namely that they intertwine $U_q(su(2)_k)$ modules. We construct the screening charge and present a formula for the n-point function. Specializing to $j=1/2$ we construct all VOs and CVOs explicitly. The existence of the CVO allows us to place the calculation of the two-point function on the same footing as $k=1$; that is, it is obtained without screening currents and involves only a single integral from the CVO. This integral is evaluated and the resulting function is shown to obey the q-KZ equation and to reduce simply to both the expected $k=1$ and $q=1$ limits.Comment: 20 pages, LaTex. Minor change

PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain

We investigate the PT-symmetry of the quantum group invariant XXZ chain. We show that the PT-operator commutes with the quantum group action and also discuss the transformation properties of the Bethe wavefunction. We exploit the fact that the Hamiltonian is an element of the Temperley-Lieb algebra in order to give an explicit and exact construction of an operator that ensures quasi-Hermiticity of the model. This construction relys on earlier ideas related to quantum group reduction. We then employ this result in connection with the quantum analogue of Schur-Weyl duality to introduce a dual pair of C-operators, both of which have closed algebraic expressions. These are novel, exact results connecting the research areas of integrable lattice systems and non-Hermitian Hamiltonians.Comment: 32 pages with figures, v2: some minor changes and added references, version published in JP

G_2^1 Affine Toda Field Theory: A Numerical Test of Exact S-Matrix results

We present the results of a Monte--Carlo simulation of the $G_2^{(1)}$ Affine Toda field theory action in two dimensions. We measured the ratio of the masses of the two fundamental particles as a function of the coupling constant. Our results strongly support the conjectured duality with the $D_4^{(3)}$ theory, and are consistent with the mass formula of Delius et al.Comment: 5 pages, LaTeX, DTP-9223, DAMTP-92-4

Evaluation and Utilization of Allelopathic Festuca rubra Turfgrass Cultivars for Alternative Weed Management Strategies

Recent experiments in Ithaca and Riverhead NY have shown that fine fescue cultivars Intrigue, Reliant, and Oxford were most suppressive in field and laboratory settings due to their allelopathic activity and their ability to establish readily in a field setting. The cultivars Treasure and Boreal were least weed suppressive in both sites in 2 years of replicated trials. Mode of action studies would suggest the inhibitor(s) in the root exudate act upon photosynthesis or respiration or possibly both. Current anatomical studies suggest root exudates are produced in actively dividing root cells and are stored until extrusion from roots in osmiophilic inclusions in root cells. The structural elucidation studies performed using GC and HPLC coupled to mass spectrometry suggest that the components of the root exudates may be steroidal in nature. Purification and structural elucidation work is ongoing

Evaluation and Utilization of Allelopathic Festuca rubra Turfgrass Cultivars and Selected Groundcovers for Alternative Weed Management Strategies in the Landscape

ReportThe development of alternative weed management strategies in landscape and turf settings involves the use and implementation of novel bio-control practices which can provide efficaceous control over the course of the growing season. Use of pathogenic organisms to control weeds has not proven particularly effective, due to problems in obtaining consistent control and difficulty in formulation of biocontrol organisms. Organically derived products, such as corn gluten or cramby meal, have also not provided consistent or inexpensive control, especially in commercial settings such as golf courses, parks and athletic fields where complete control is often desirable. One novel approach which shows strong potential is the selection, development and use of allelopathic or weed suppressive turfgrasses or groundcovers to naturally control annual weeds in the landscape, without the use of herbicides. Fescues, especially Festuca rubra spp., produce secondary products known as allelochemicals with potent ability to suppress weed seed germination and growth