Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero–Moser model

We consider solutions of the matrix KP hierarchy that are elliptic functions first hierarchical time $t_1=x$. It is known poles $x_i$ and residues at $\rho_i^{\alpha \beta}=a_i^{\alpha}b_i^{\beta}$ such as $t_2$ move particles spin generalization Calogero-Moser model (elliptic Gibbons-Hermsen model). In this paper we establish correspondence with for whole hierarchy. Namely, show dynamics respect to $k$-th Hamiltonian $H_k$ obtained via an expansion spectral curve near marked points. The Hamiltonians identified system coordinates degrees freedom $a_i^{\alpha}, \, b_i^{\beta}$.