Solving 3-body elliptic Calogero model

par Prof. Alexander TURBINER (Nuclear Science Institute, National University of Mexico & IHES)

jeudi 30 oct. 2014, 14:30 → 15:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

It is found a change of variables transforming A₂ elliptic one-parametric Hamiltonian (in other words, 3-body elliptic Calogero Hamiltonian, or two-dimensional Lame operator) into algebraic differential operator with polynomial coefficients. It is shown the A₂ elliptic model is equivalent to gl(3) quantum top and its parameter is determined by spin of gl(3) representation. It is found the discrete values of the parameter for which two-dimensional Lame operator has polynomial eigenfunctions.