  Starting from the deformed current-counting transition matrix for the open
boundary ASEP, we prove that with a further deformation, the symmetric
Koornwinder polynomials for partitions with equal row lengths appear as the
normalisation of the twice deformed ground state. We give a matrix product
construction for this ground state and the corresponding symmetric Koornwinder
polynomials. Based on the form of this construction and numerical evidence, we
conjecture a relation between the generating function of the cumulants of the
current, and a certain limit of the symmetric Koornwinder polynomials.
