  The generic Hecke algebra for the hyperoctahedral group, i.e. the Weyl group
of type B, contains the generic Hecke algebra for the symmetric group, i.e. the
Weyl group of type A, as a subalgebra. Inducing the index representation of the
subalgebra gives a Hecke algebra module, which splits multiplicity free. The
corresponding zonal spherical functions are calculated in terms of q-Krawtchouk
polynomials. The result covers a number of previously established
interpretations of (q-)Krawtchouk polynomials on the hyperoctahedral group,
finite groups of Lie type, hypergroups and the quantum SU(2) group. Jimbo's
analogue of the Frobenius-Schur-Weyl duality is a key ingredient in the proof.
