  We study convolution algebras associated with Heckman-Opdam polynomials. For
root systems of type BC we derive three continuous classes of positive
convolution algebras (hypergroups) by interpolating the double coset
convolution structures of compact Grassmannians U/K with fixed rank over the
real, complex or quaternionic numbers. These convolution algebras are linked to
explicit positive product formulas for Heckman-Opdam polynomials of type BC,
which occur for certain discrete multiplicities as the spherical functions of
U/K. These results complement those of a recent paper by the second author for
the non-compact case.
