ON THE 2-GAP LOCUS FOR THE ELLIPTIC CALOGERO-MOSER MODEL

We give an analytical description of the locus of the two-gap elliptic potentials associated with the corresponding flow of the Calogero-Mos er system. We start with the description of Treibich-Verdier two-gap e lliptic potentials. The explicit formulae for the covers, wavefunction s and Lame polynomials are derived, together with a new Lax representa tion for the particle dynamics on the locus. We then consider more gen eral potentials within the Weierstrass reduction theory of theta funct ions to lower genera. The reduction conditions in the moduli space of the genus-2 algebraic curves are given. This is a subvariety of the Hu mbert surface, which can be singled cut by the condition of the vanish ing of some theta constants.