  Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van
Diejen we define a 6-parameter double affine Hecke algebra and establish its
basic structural properties, including the existence of an involution. We
relate the algebra to (symmetric and nonsymmetric) Koornwinder polynomials via
the method of intertwiners and, as a consequence, obtain a proof of Macdonald's
duality conjecture for Koornwinder polynomials. Combined with earlier work of
van Diejen this completely settles all the outstanding conjectures of Macdonald
and Koornwinder about these polynomials.
