Yang-Baxter algebras based on the two-colour BWM algebra

We present a Baxterization of a two-colour generalization of the Birman--Wenzl--Murakami (BWM) algebra. Appropriately combining two RSOS-type representations of the ordinary BWM algebra, we construct representations of the two-colour algebra. Using the Baxterization, this provides new RSOS-type solutions to the Yang--Baxter equation.Comment: 14 pages, uuencoded compressed PostScript fil

Order Parameters of the Dilute A Models

The free energy and local height probabilities of the dilute A models with broken \Integer_2 symmetry are calculated analytically using inversion and corner transfer matrix methods. These models possess four critical branches. The first two branches provide new realisations of the unitary minimal series and the other two branches give a direct product of this series with an Ising model. We identify the integrable perturbations which move the dilute A models away from the critical limit. Generalised order parameters are defined and their critical exponents extracted. The associated conformal weights are found to occur on the diagonal of the relevant Kac table. In an appropriate regime the dilute A$_3$ model lies in the universality class of the Ising model in a magnetic field. In this case we obtain the magnetic exponent $\delta=15$ directly, without the use of scaling relations.Comment: 53 pages, LaTex, ITFA 93-1

Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture

We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case

New Finite Rogers-Ramanujan Identities

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson's transformation formula by specialization or through Bailey's method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.Comment: 19 pages. to appear in Ramanujan

Discrete Holomorphicity at Two-Dimensional Critical Points

After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects whose correlation functions satisfy a discrete version of the Cauchy-Riemann relations. Their existence appears to have a deep relation with the integrability of the model, and they are presumably the lattice versions of the truly holomorphic observables appearing in the conformal field theory (CFT) describing the continuum limit. This hypothesis sheds light on the connection between CFT and integrability, and, if verified, can also be used to prove that the scaling limit of certain discrete curves in these models is described by Schramm-Loewner evolution (SLE).Comment: Invited talk at the 100th Statistical Mechanics Meeting, Rutgers, December 200

Inhibition of bispecific monoclonal antibody (bsAb)-targeted cytolysis by human anti-mouse antibodies in ovarian carcinoma patients treated with bsAb-targeted activated T-lymphocytes

T lymphocytes of 8 patients with ovarian cancer were targeted to the tumor cells using F(ab')2 fragments of a bispecific monoclonal antibody (bsAb), specific for CD3 (a component of the T lymphocyte receptor for antigen) and for the folate receptor MOv 18 (overexpressed by ovarian carcinoma cells) as part of a phase l/II study. Phase I (days 0 to 3) consisted of increasing intraperitoneal (i.p.) numbers (106−109) of bsAbtargeted T lymphocytes plus lowdose interleukin-2 (IL-2). Phase II (days 6 to 13, and 27 to 33) consisted of daily i.p. infusions of 109 targeted T lymphocytes, 2 mg soluble bsAb, and lowdose IL-2. Using enzymelinked immunosorbent assays (ELISA), human antimouse antibodies (HAMA) were detected in all patients: in the serum from day 13 onwards and in the peritoneal fluid from day 20 onwards. A significant proportion of the HAMA appeared to be directed against the idiotypes of the bsAb specific for CD3 and MOv18, as suggested by (I) the clearly higher ELISA titers against OC/TR bsAb as compared to those against a monoclonal antibody (MAb) with unrelated specificity, and (2) failure to abrogate the capacity of peritoneal fluid containing HAMA to block the binding of OC/TR bsAb to MOv18+ or CD3+ cells by absorption of human antimouse IgG-framework antibodies in peritoneal fluid to immobilized mouse IgG. The OC/TR-targeted cytolysis of the MOv18+ ovarian carcinoma cell line lgrov-1 by autologous T lymphocytes was inhibited by peritoneal fluid samples containing relatively high HAMA titers. Such inhibitory activity was never detected at the start of phase II, but coincided with the last series of i.p. infusions of targeted T lymphocytes in 2 patients

Local but no systemic immunomodulation by intraperitoneal treatment of advanced ovarian cancer with autologous T lymphocytes re-targeted by a bi-specific monoclonal antibody

We have reported a 27% overall anti-tumor response using i.p. immunotherapy of advanced ovarian carcinoma with autologous, ex vivo expanded, T lymphocytes re-targeted with bi-specific monoclonal antibody OC/TR, combined with soluble OC/TR and low-dose recombinant interleukin-2 (IL-2). This treatment had no effect on extraperitoneal disease. Therefore we studied in 13 patients whether this immunotherapeutic protocol resulted only in local or also in systemic immunomodulation. The phenotype of the ex vivo expanded lymphocytes was mainly CD3+, 4-, 8+, 16-, 56-. Their OC/TR-re-targeted cytolytic activity against Igrov-1 ovarian-carcinoma cells was approximately as high in responders as in non-responders. Following most therapeutic cycles, the immunophenotype of lymphocytes recovered from the peritoneal fluid was similar to that of the infused T cells (i.e., mainly CD3+, 4-, 8+) and they were coated with OC/TR. However, cytolytic activity of the recovered lymphocytes against Igrov- 1 cells was low in direct assays, and only slightly increased after additional in vitro re-targeting with OC/TR. Systemically, the i.p. immunotherapy resulted in a transient lymphopenia lasting for about 7 days, low (i.e., 5 to 13 ng/ml) serum concentrations of free, functional OC/TR, and very weak coating of circulating T lymphocytes with OC/TR. These peripheral-blood T lymphocytes did not exert OC/TR-re-targeted cytolytic activity. Thus, locoregional OC/TR-re-targeted cellular immunotherapy resulted in substantial local immunomodulation and anti-tumor effects but virtually no systemic immunomodulation

The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$ to a two-colour loop model on the square lattice is established. For non-interacting fermions this model reduces to an exactly solved loop model which is known to be a free fermion model. The two-colour loop model equivalent to the Thirring model can also be understood as a 4-state 49-vertex model.Comment: 29 pages LaTe

Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model

We generalize the string functions C_{n,r}(tau) associated with the coset ^sl(2)_k/u(1) to higher string functions A_{n,r}(tau) and B_{n,r}(tau) associated with the coset W(k)/u(1) of the W-algebra of the logarithmically extended ^sl(2)_k conformal field model with positive integer k. The higher string functions occur in decomposing W(k) characters with respect to level-k theta and Appell functions and their derivatives (the characters are neither quasiperiodic nor holomorphic, and therefore cannot decompose with respect to only theta-functions). The decomposition coefficients, to be considered ``logarithmic parafermionic characters,'' are given by A_{n,r}(tau), B_{n,r}(tau), C_{n,r}(tau), and by the triplet \mathscr{W}(p)-algebra characters of the (p=k+2,1) logarithmic model. We study the properties of A_{n,r} and B_{n,r}, which nontrivially generalize those of the classic string functions C_{n,r}, and evaluate the modular group representation generated from A_{n,r}(tau) and B_{n,r}(tau); its structure inherits some features of modular transformations of the higher-level Appell functions and the associated transcendental function Phi.Comment: 34 pages, amsart++, times. V2: references added; minor changes; some nonsense in B.3.3. correcte