Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

Non-Polynomial Realizations of W-Algebras

Relaxing first-class constraint conditions in the usual Drinfeld-Sokolov Hamiltonian reduction leads, after symmetry fixing, to realizations of W algebras expressed in terms of all the J-current components. General results are given for G a non exceptional simple (finite and affine) algebra. Such calculations directly provide the commutant, in the (closure of) G enveloping algebra, of the nilpotent subalgebra $G_-$, where the subscript refers to the chosen gradation in G. In the affine case, explicit expressions are presented for the Virasoro, $W_3$, and Bershadsky algebras at the quantum level.Comment: 33 pages, LaTeX file, minor LaTex error correcte

W-realization of Lie algebras: application to so(4,2) and Poincare algebras

The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a "canonical" differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated- to the induced representation technic.Comment: LaTeX, 18 page

Hidden nonlinear supersymmetries in pure parabosonic systems

The existence of intimate relation between generalized statistics and supersymmetry is established by observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear superalgebra. The nonlinear supersymmetry of parabosonic systems may be realized, in turn, by modifying appropriately the usual supersymmetric quantum mechanics. The relation of nonlinear parabosonic supersymmetry to the Calogero-like models with exchange interaction and to the spin chain models with inverse-square interaction is pointed out.Comment: 20 pages, one reference corrected, to appear in Int. J. Mod. Phys.

Finite W Algebras and Intermediate Statistics

New realizations of finite W algebras are constructed by relaxing the usual constraint conditions. Then, finite W algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well-adapted for a possible generalization of the anyon statistics.Comment: 16 pp., Latex, Preprint ENSLAPP-489/9

Phase transitions between single- and double-layered smectic structures in binary mixtures of cyano-mesogens

Binary mixtures of mesogens which exhibit respectively single-layered (A 1), double layered (A2) and partially double layered (A d) smectic phases show abrupt A2-A1 or A2-Ad transitions as a function of concentration. Double layered structures imply the formation of dimerized entities and the possibility of dimerization is discussed in terms of the amphiphilic nature of the molecules in the binary mixture (symmetrical and dissymmetrical polar mesogens). The results are analysed with respect to the thermal stability of the A 2 phase when defects are introduced in the polar interface by adding non-polar symmetrical mesogens.Des mélanges binaires de mésogènes présentant respectivement des phases smectiques monocouches (A1), bicouches (A2) et partiellement bicouches (Ad) permettent de mettre en évidence en fonction de la concentration des transitions brusques A2-A1 ou A 2-Ad. La structure bicouche implique un processus de dimérisation des entités mésogènes qui est discuté en fonction du caractère amphipathique des molécules (molécules polaires symétriques et dissymétriques). La stabilité de la phase bicouche est également analysée lorsque l'on introduit une perturbation au niveau de l'interface polaire par adjonction de molécules non polaires

The Social and Cultural Context of Coping with Sickle Cell Disease: II. The Role of Financial Hardship in Adjustment to Sickle Cell Disease

Recent evidence on the negative psychological effects of poverty suggests that economic status alone might account for the adjustment problems attributed to sickle cell disease (SCD). The relationship of SCD and financial hardship to adjustment was examined in 327 ill children and their parents. SCD and hardship contributed independently to impaired child and parental functioning. For parents, illness severity had more negative effects than did financial hardship, but forPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66919/2/10.1177_0095798499025003003.pd

The Social and Cultural Context of Coping with Sickle Cell Disease: III. Stress, Coping Tasks, Family Functioning, and Children’s Adjustment

Conceptions of individual and family coping with sickle cell disease (SCD) must incorporate several disease and sociocultural factors. This article proposes an integrative model and tests the relative contribution of model parameters to the prediction of social, academic, and psychological adjustment of children with SCD. The individual coping and family functioning variables most highly predictive of the child’s psychological outcomes (anxiety, depression, and positive mood) include parental psychological functioning, maturity demands made of the ill child, and the quality of relations with parents and siblings. Academic adjustment was significantly predicted by parental academic expectations and by the child’s rejection of a restrictive sick role. Competent social functioning also was predicted by the extent to which the ill child rejected the role of being sick.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67288/2/10.1177_0095798499025003006.pd

Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy

We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian generators in terms of deformed oscillators.Comment: LaTeX2e, 10 pages, Talk presented by E. Ragoucy at ACTP-Nankai Symposium on Yang-Baxter systems, non linear models and their applications, Seoul (Korea) October 20-23, 199