A. Nishino et Y. Komori, An algebraic approach to Macdonald-Koornwinder polynomials: Rodrigues-typeformula and inner product identity, J MATH PHYS, 42(10), 2001, pp. 5020-5046
We study Macdonald-Koornwinder polynomials in the context of double affine
Hecke algebras. Nonsymmetric Macdonald-Koornwinder polynomials are construc
ted by use of raising operators provided by a representation theory of the
double affine Hecke algebra associated with A(2l)((2))-type affine root sys
tem. This enables us to evaluate diagonal terms of scalar products of the n
onsymmetric polynomials algebraically. The Macdonald-Koornwinder polynomial
s are expressed by linear combinations of the nonsymmetric counterparts. We
show a new proof of the inner product identity of the Macdonald-Koornwinde
r polynomials without Opdam-Cherednik's shift operators. (C) 2001 American
Institute of Physics.