Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

The development of an advanced system to cool a man in a pressure suit

Conductive cooling system for cooling man in pressurized space sui

SOS model partition function and the elliptic weight functions

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_{q}(\hat{\mathfrak{sl}}_{2})$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag

Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two references to Awata,H. et al adde

Elliptic quantum groups Eτ,η(sl2)E_{\tau,\eta}(sl_2) and quasi-Hopf algebras

We construct an algebra morphism from the elliptic quantum group $E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in higher genus'' studied by V. Rubtsov and the first author. This provides an embedding of $E_{\tau,\eta}(sl_2)$ in an algebra ``with central extension''. In particular we construct $L^{\pm}$-operators obeying a dynamical version of the Reshetikhin--Semenov-Tian-Shansky relations. To do that, we construct the factorization of a certain twist of the latter algebra, that automatically satisfies the ``twisted cocycle condition'' of O. Babelon, D. Bernard and E. Billey, and therefore provides a solution of the dynamical Yang-Baxter equation.Comment: Amslatex file, 43 pages, references adde

The Canonical Structure of Wess-Zumino-Witten Models

The phase space of the Wess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group $G$ is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets of the Wess-Zumino-Witten model. We also study the canonical structure of the supersymmetric and the gauged Wess-Zumino-Witten models.Comment: 16pp (revised version - two new sections added and relation with other recent work discussed