A determinant formula for a holonomic q-difference system associated with Jackson integrals of type BCn

A Jackson integral of type BCn is a multisum generalization of the very-well-poised-balanced basic hypergeometric series. We state an explicit product formula for the determinant of a matrix with entries given by the BCn type Jackson integrals. In order to show this, we treat the determinant as a solution of a holonomic q-difference equation. In particular we give the q-difference equation explicitly as a two-term recurrence relation, which the determinant satisfies, by introducing a set of new symmetric polynomials via the symplectic Schur functions.