  We present a one-parameter family of constant solutions of the reflection
equation and define a family of quantum complex Grassmannians endowed with a
transitive action of the quantum unitary group. By computing the radial part of
a suitable Casimir operator, we identify the zonal spherical functions (i.e.
infinitesimally bi-invariant matrix coefficients of finite-dimensional
irreducible representations) as multivariable Askey-Wilson polynomials
containing two continuous and two discrete parameters.
