A Littlewood–Richardson rule for Koornwinder polynomials

Koornwinder polynomials are q-orthogonal equipped with extra five parameters and the $$B C_n$$ -type Weyl group symmetry, which were introduced by (Contemp Math 138:189–204, 1992) as multivariate analogue of Askey–Wilson polynomials. They now understood Macdonald associated affine root system type $$(C^\vee _n,C_n)$$ via Macdonald–Cherednik theory double Hecke algebras. In this paper, we give explicit formulas Littlewood–Richardson coefficients for polynomials, i.e., structure constants product invariant Our natural -analogue Yip’s alcove-walk (Math Z 272:1259–1290, 2012) given in case reduced systems.