95 research outputs found
Hidden symmetry of the quantum Calogero-Moser system
Hidden symmetry of the quantum Calogero-Moser system with the inverse-square
potential is explicitly demonstrated in algebraic sense. We find the underlying
algebra explaining the super-integrability phenomenon for this system.
Applications to related multi-variable Bessel functions are also discussed.Comment: 16 pages, latex, no figure
Generalized Calogero-Moser systems from rational Cherednik algebras
We consider ideals of polynomials vanishing on the W-orbits of the
intersections of mirrors of a finite reflection group W. We determine all such
ideals which are invariant under the action of the corresponding rational
Cherednik algebra hence form submodules in the polynomial module. We show that
a quantum integrable system can be defined for every such ideal for a real
reflection group W. This leads to known and new integrable systems of
Calogero-Moser type which we explicitly specify. In the case of classical
Coxeter groups we also obtain generalized Calogero-Moser systems with added
quadratic potential.Comment: 36 pages; the main change is an improvement of section 7 so that it
now deals with an arbitrary complex reflection group; Selecta Math, 201
Duality for Jacobi group orbit spaces and elliptic solutions of the WDVV equations
From any given Frobenius manifold one may construct a so-called dual
structure which, while not satisfying the full axioms of a Frobenius manifold,
shares many of its essential features, such as the existence of a prepotential
satisfying the WDVV equations of associativity. Jacobi group orbit spaces
naturally carry the structures of a Frobenius manifold and hence there exists a
dual prepotential. In this paper this dual prepotential is constructed and
expressed in terms of the elliptic polylogarithm function of Beilinson and
Levin
Investigation the role of religious organizations in system of general education: forms of state- confessional interaction
The purpose of the this was aimed at conducting a system analysis of the forms of interaction between religious organizations and modern states implementing the secular model regarding the regulation of religion component in the field of general educatio
Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the
KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring
of translational operators in the spectral parameter. In the rational limit,
these translational operators converge to the differential operators in the
spectral parameter previously discussed as part of the theory of
"bispectrality". Consequently, these translational operators can be seen as
demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems
Effect of heavy-ion irradiation on the nanoscale state of advanced reactor ferritic-martensitic steels
Maximal Abelian Subgroups of the Isometry and Conformal Groups of Euclidean and Minkowski Spaces
The maximal Abelian subalgebras of the Euclidean e(p,0) and pseudoeuclidean
e(p,1)Lie algebras are classified into conjugacy classes under the action of
the corresponding Lie groups E(p,0) and E(p,1), and also under the conformal
groups O(p+1,1) and O(p+1,2), respectively. The results are presented in terms
of decomposition theorems. For e(p,0) orthogonally indecomposable MASAs exist
only for p=1 and p=2. For e(p,1), on the other hand, orthogonally
indecomposable MASAs exist for all values of p. The results are used to
construct new coordinate systems in which wave equations and Hamilton-Jacobi
equations allow the separation of variables.Comment: 31 pages, Latex (+ latexsym
BPS States in Omega Background and Integrability
We reconsider string and domain wall central charges in N=2 supersymmetric
gauge theories in four dimensions in presence of the Omega background in the
Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of
the corresponding topological defects in the theory - vortices and domain
walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy
effective theory living on the BPS vortex in N=2 Supersymmetric Quantum
Chromodynamics (SQCD). We discuss some aspects of the brane realization of the
dualities between various quantum integrable models. A chain of such dualities
enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos
correcte
On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh’s formalism, we construct commuting Hamiltonian functions on the phase space and identify one of the flows with the spin Ruijsenaars–Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly
New Integrable Generalizations of the CMS Quantum Problem and Deformations of Root Systems
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