178,885 research outputs found
Factorization in generalized Calogero-Moser spaces
No full textUsing a recent construction of Bezrukavnikov and Etingof we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = S_n, this confirms a conjecture of Etingof and Ginzburg
On the Calogero-Moser space associated with dihedral groups
No full textInternational audienceUsing the geometry of the associated Calogero-Moser space, R. Rouquier and the author have attached to any finite complex reflection group several notions (Calogero-Moser left, right or two-sided cells, Calogero-Moser cellular characters), completing the notion of Calogero-Moser families defined by Gordon. If moreover is a Coxeter group, they conjectured that these notions coincide with the analogous notions defined using the Hecke algebra by Kazhdan and Lusztig (or Lusztig in the unequal parameters case). In the present paper, we aim to investigate these conjectures whenever is a dihedral group
TOTALLY CLASSICAL CALOGERO MODEL
No full textInternational audienceWe show that the standard Calogero Lax matrix can be interpreted as a function on the fuzzy sphere and the Avan–Talon r-matrix as a function on the direct product of two fuzzy spheres. We calculate the limiting Lax function and r-function when the fuzzy sphere tends to the ordinary sphere and we show that they define an integrable model interpreted as a large N Calogero model by Bordemann, Hoppe and Theisen
Quadratic algebra associated with rational Calogero-Moser models
No full textInternational audienceClassical Calogero–Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r−1 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebrastructure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebrastructure for quantum rational Calogero–Moser models based on any root systems
Guido Calogero e la rivista "liberalsocialismo"
No full textPolitical Thought of Guido Calogero after second world war in Ital
Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero-Moser model
No full textWe consider 1+1 field generalization of the elliptic Calogero-Moser model. It
is shown that the Lax connection satisfies the classical non-ultralocal
-matrix structure of Maillet type. Next, we consider 1+1 field analogue of
the spin Calogero-Moser model and its multipole (or multispin) extension.
Finally, we discuss the field analogue of the classical IRF-Vertex
correspondence, which relates utralocal and non-ultralocal -matrix
structures.Comment: 26 pages, some comments and Appendix adde
The developmental effects of media-ideal internalization and self-objectification processes on adolescents’ negative body-feelings, dietary restraint, and binge eating
No full textDespite accumulated experimental evidence of the negative effects of exposure to media-idealized images, the degree to which body image, and eating related disturbances are caused by media portrayals of gendered beauty ideals remains controversial. On the basis of the most up-to-date meta-analysis of experimental studies indicating that media-idealized images have the most harmful and substantial impact on vulnerable individuals regardless of gender (i.e., “internalizers” and “self-objectifiers”), the current longitudinal study examined the direct and mediated links posited in objectification theory among media-ideal internalization, self-objectification, shame and anxiety surrounding the body and appearance, dietary restraint, and binge eating. Data collected from 685 adolescents aged between 14 and 15 at baseline (47 % males), who were interviewed and completed standardized measures annually over a 3-year period, were analyzed using a structural equation modeling approach. Results indicated that media-ideal internalization predicted later thinking and scrutinizing of one’s body from an external observer’s standpoint (or self-objectification), which then predicted later negative emotional experiences related to one’s body and appearance. In turn, these negative emotional experiences predicted subsequent dietary restraint and binge eating, and each of these core features of eating disorders influenced each other. Differences in the strength of these associations across gender were not observed, and all indirect effects were significant. The study provides valuable information about how the cultural values embodied by gendered beauty ideals negatively influence adolescents’ feelings, thoughts and behaviors regarding their own body, and on the complex processes involved in disordered eating. Practical implications are discussed
The Extended conformal theory of the Calogero-Sutherland model
No full textWe describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented
The quantum angular Calogero-Moser model
No full textThe rational Calogero–Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the ‘angular Calogero–Moser model’ on the sphere S^{n-1}. We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a ‘relative angular Calogero–Moser model’, which is analyzed in parallel. We generalize our considerations to the Calogero–Moser models associated with Coxeter
groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin–Calogero system
R-matrix Dunkl operators and spin Calogero-Moser system
No full textWe construct a quantum integrable model which is an R-matrix generalization of the Calogero-Moser system, based on the Baxter–Belavin elliptic R-matrix.
This is achieved by introducing R-matrix Dunkl operators so that commuting quantum
spin Hamiltonians can be obtained from symmetric combinations of those. We construct quantum and classical R-matrix Lax pairs for these systems. In particular, we
recover in a conceptual way the classical R-matrix Lax pair of Levin, Olshanetsky, and
Zotov, as well as the quantum Lax pair found by Grekov and Zotov. Finally, using
the freezing procedure, we construct commuting conserved charges for the associated
quantum spin chain proposed by Sechin and Zotov, and introduce its integrable deformation. Our results remain valid when the Baxter–Belavin R-matrix is replaced by any
of the trigonometric R-matrices found by Schedler and Polishchuk in their study of the
associative Yang–Baxter equation
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