Integrals of motion of classical lattice sine-Gordon system

We compute the local integrals of motions of the classical limit of the lattice sine-Gordon system, using a geometrical interpretation of the local sine-Gordon variables. Using an analogous description of the screened local variables, we show that these integrals are in involution. We present some remarks on relations with the situation at roots of 1 and results on another latticisation (linked to the principal subalgebra of $\widehat{s\ell}_{2}$ rather than the homogeneous one). Finally, we analyse a module of ``screened semilocal variables'', on which the whole $\widehat{s\ell}_{2}$ acts.Comment: (references added

Two character formulas for sl2^\hat{sl_2} spaces of coinvariants

We consider $\hat{sl_2}$ spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra U(sl_2\otimes\C[t]). The first one is generated by $sl_2\otimes t^N$, and the second one is generated by $e\otimes P(t), f\otimes R(t)$ where $P(t), R(t)$ are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and $q$-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion product of $sl_3$-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.Comment: LaTeX, 22 pages; very minor change

Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras

We introduce a functional realization of the Hamiltonian structure on the moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup in SL_n. We also introduce a construction of the corresponding quantum algebras.Comment: 20 pages, Amstex, minor change

Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation

We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra $n_+$ of affine Lie algebra $\hat {sl}_2$ on a Maxwell-Bloch phase space treated as a homogeneous space of $n_+$. A space of local integrals of motion is described using cohomology methods. We show that hamiltonian flows associated to the Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are identified with an infinitesimal action of an abelian subalgebra of the nilpotent subalgebra $n_+$ on a Maxwell- Bloch phase space. Possibilities of quantization and latticization of Maxwell-Bloch equation are discussed.Comment: 16 pages, no figures, plain TeX, no macro

Explicit description of twisted Wakimoto realizations of affine Lie algebras

In a vertex algebraic framework, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a complex simple Lie algebra. This yields generalized free field realizations of the twisted and untwisted affine Lie algebras in any gradation. The free field form of the twisted Sugawara formula and examples are also exhibited.Comment: 24 pages, LaTeX, v2: small corrections in appendix

Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)

It is shown that the elliptic algebra A_{p,q}(sl(2)_c) has a non trivial center at the critical level $c=-2$, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric algebras. A family of Poisson structures indexed by a non-negative integer $k$ is constructed on this center.Comment: LaTeX 2.09 Document (should be run twice

Computerised tomography indices of raised intracranial pressure and traumatic brain injury severity in a New Zealand sample

After traumatic brain injury (TBI) complex cellular and biochemical processes occur¹ including changes in blood flow and oxygenation of the brain; cerebral swelling; and raised intracranial pressure (ICP).² This can dramatically worsen the damage³ and contributes to mortality