ar X iv : m at h - ph / 0 30 70 05 v 1 2 J ul 2 00 3 INDUCED REPRESENTATIONS OF CAYLEY – KLEIN ORTHOGONAL GROUPS

X iv : m at h - ph / 0 30 70 08 v 1 2 J ul 2 00 3 IRREDUCIBLE REPRESENTATIONS OF CAYLEY – KLEIN ORTHOGONAL ALGEBRAS

Multidimensional contractions of irreducible representations of the Cayley–Klein orthogonal algebras in Gel'fand–Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be iso-morphic. In this case method of transitions describes the same reducible representations in different basises, say discrete and continuons ones.

ar X iv : m at h - ph / 0 30 70 15 v 1 8 J ul 2 00 3 Integrable geodesic flows on Riemannian manifolds : Construction and Obstructions ∗ Alexey

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

ar X iv : 0 70 7 . 03 46 v 1 [ m at h - ph ] 3 J ul 2 00 7 THE ONE - DIMENSIONAL SCHRÖDINGER - NEWTON EQUATIONS

We prove an existence and uniqueness result for ground states of one-dimensional Schrödinger-Newton equations.

ar X iv : m at h / 06 07 13 0 v 1 [ m at h . A G ] 5 J ul 2 00 6 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

ar X iv : m at h - ph / 0 70 30 43 v 3 2 8 O ct 2 00 7 RANDOM MATRICES , NON - BACKTRACKING WALKS , AND ORTHOGONAL POLYNOMIALS

Several well-known results from the random matrix theory, such as Wigner’s law and the Marchenko–Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the limiting spectral measure play a rôle in this approach.