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

Representation Theory