Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
http://dspace.nbuv.gov.ua:80/handle/123456789/145983
2024-03-28T15:02:39ZA Journey Between Two Curves
http://dspace.nbuv.gov.ua:80/handle/123456789/147995
A Journey Between Two Curves
Cherkis, S.A.
A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the system of Nahm equations is closely related to the Hitchin system, the curves appearing in these two cases have very different nature. The former can be described in terms of some classical scattering problem while the latter provides a solution to some Seiberg-Witten gauge theory. This note identifies the setup in which one can formulate the question of relating the two curves.
2007-01-01T00:00:00ZDeformation Quantization in White Noise Analysis
http://dspace.nbuv.gov.ua:80/handle/123456789/147837
Deformation Quantization in White Noise Analysis
Léandre, R.
We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.
2007-01-01T00:00:00ZBethe Ansatz for the Ruijsenaars Model of BC₁-Type
http://dspace.nbuv.gov.ua:80/handle/123456789/147836
Bethe Ansatz for the Ruijsenaars Model of BC₁-Type
Chalykh, O.
We consider one-dimensional elliptic Ruijsenaars model of type BC₁. It is given by a three-term difference Schrödinger operator L containing 8 coupling constants. We show that when all coupling constants are integers, L has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the A₁-case.
2007-01-01T00:00:00ZThe 6 Vertex Model and Schubert Polynomials
http://dspace.nbuv.gov.ua:80/handle/123456789/147835
The 6 Vertex Model and Schubert Polynomials
Lascoux, A.
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.
2007-01-01T00:00:00Z