BC infinity Calogero-Moser operator and super Jacobi polynomials

An infinite-dimensional version of Calogero–Moser operator of BC -type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov's binomial formula. We use this to describe all the ideals linearly generated by the Jacobi symmetric functions and show that the deformed BC(m,n)BC(m,n) Calogero–Moser operators, introduced in our earlier work, appear here in a natural way as the restrictions of the BC∞BC∞ operator to the corresponding finite-dimensional subvarieties. As a corollary we have the integrability of these quantum systems and all the main formulas for the related super Jacobi polynomials.