q-difference shift for a BCn-type Jackson integral arising from ‘elementary’ symmetric polynomials

We study a q-difference equation of a BCn-type Jackson integral introduced by van Diejen. The BCn-type Jackson integral is a multiple q-series generalized from a q-analogue of Selberg's integral. The equation is characterized by some new symmetric polynomials defined via symplectic Schur functions. As an application, we give another proof of a product formula for the BCn-type Jackson integral, which is equivalent to the so-called q-Macdonald–Morris identity for the root system BCn first obtained by Gustafson.