Integrability and Transition Coefficients Related to Jack Polynomials

Integrability plays a central role in solving many body problems in physics. The explicit construction of the Jack polynomials is an essential ingredient in solving the Calogero-Sutherland model, which is a one-dimensional integrable system. Starting from a special class of the Jack polynomials associated to the hook Young diagram, we find a systematic way in the explicit construction of the transition coefficients in the power-sum basis, which is closely related to a set of mutually commuting operators, i.e. the conserved charges.