An algebraic approach to Macdonald-Koornwinder polynomials: Rodrigues-type formula and inner product identity

We study Macdonald-Koornwinder polynomials in the context of double affine Hecke algebras. Nonsymmetric Macdonald-Koornwinder polynomials are constructed by use of raising operators provided by a representation theory of the double affine Hecke algebra associated with A(2l)((2))-type affine root system. This enables us to evaluate diagonal terms of scalar products of the nonsymmetric polynomials algebraically. The Macdonald-Koornwinder polynomials are expressed by linear combinations of the nonsymmetric counterparts. We show a new proof of the inner product identity of the Macdonald-Koornwinder polynomials without Opdam-Cherednik's shift operators. (C) 2001 American Institute of Physics.