252 research outputs found
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 , where the subscript refers to the
chosen gradation in G. In the affine case, explicit expressions are presented
for the Virasoro, , 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 mésogÚnes 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 mésogÚnes qui est discuté en fonction du caractÚre 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 Childrenâs 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 childâs 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 childâs 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
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