I. | May 29, 2004, 11:00-12:15, RIMS, Room 206 | |
DR Rei Inoue Yamazaki ( RIMS, Kyoto University ) | ||
TITLE: | ||
Matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice | ||
ABSTRACT: | ||
Consider a gauge equivalence class M of polynomial matrices of a spectral
parameter, and let X be the algebraic curve given by the common
characteristic equation for M. It is known that M is isomorphic to the
affine part of the Jacobi variety, J_{aff}(X).
In the context of classical integrable Hamiltonian systems, an orbit in M corresponds to the level set of some Lax matrix, and J_{aff}(X) is the invariant manifold of the system. We construct a family of M and corresponded representatives explicitly by starting with certain types of Lax matrices, and study the isomorphic map from the representative to J_{aff}(X). Further we apply these to discuss the algebraic complete integrability of the extended Lotka-Volterra lattice with a periodic boundary condition. This work corresponds to a partial extension of the result by Smirnov and Zeitlin. | ||
| ||
LUNCH: 12:20-13:30 | ||
| ||
II. | May 29, 2004, 13:30-14:30, RIMS, Room 206 | |
DR Masahiro Kasatani ( Kyoto University ) | ||
TITLE: | ||
The vanishing ideal on double shifted diagonal and Jack and Macdonald polynomials | ||
ABSTRACT: | ||
We construct a ideal defined by certain zero condition on the double shifted
diagonal. We give a basis by Jack and Macdonald polynomials and its linear
combination with specialized parameters.
A character formula (Hilbert-Poincaré series) is given.
Joint work with T.Miwa, A.N.Sergeev, A.P.Veselov | ||
Research Institute for Mathematical Sciences, Kyoto University |
Anatol Kirillov |