Generalisation of the affine-type inner product construction

Let the inner product be the construction given in Theorem~, and let an affine type mean the type of an affine Weyl group or affine Hecke algebra. Inner product generalisation conjecture. The construction of the inner product in Theorem~ generalises to arbitrary affine type. This would extend the inner-product construction proved in the paper's specific affine type to all affine types.