ar X iv : m at h - ph / 0 60 40 13 v 1 6 A pr 2 00 6 Scattering matrices and Weyl functions ∗

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 40 40 45 v 1 1 9 A pr 2 00 4 On the refined 3 - enumeration of alternating sign matrices

An explicit expression for the numbers A(n, r; 3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n, r; 3)'s are represented as 1-fold sums which can also be written in terms of terminating 4 F 3 series of argument 1/4.

ar X iv : m at h - ph / 0 60 20 16 v 2 3 A pr 2 00 6 Magnetic Geodesic Flows on Coadjoint Orbits ∗ † ‡

We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.

ar X iv : m at h - ph / 0 70 10 41 v 2 1 9 A pr 2 00 7 Coupled Painlevé VI system with E ( 1 ) 6 - symmetry

We present an new system of ordinary differential equations with affine Weyl group symmetry of type E (1) 6 . This system is expressed as a Hamiltonian system of sixth order with a coupled Painlevé VI Hamiltonian. Introduction The Painlevé equations PJ (J = I, . . . ,VI) are ordinary differential equations of second order. It is known that these PJ admit the following affine Weyl group symmetri...

ar X iv : m at h - ph / 0 60 20 11 v 1 3 F eb 2 00 6 Alternative linear structures associated with regular Lagrangians . Weyl quantization and the Von Neumann uniqueness theorem

We discuss how the existence of a regular Lagrangian description on the tangent bundle T Q of some configuration space Q allows for the construction of a linear structure on T Q that can be considered as " adapted " to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the syste...