Heckman–Opdam polynomials explained

In mathematics, Heckman–Opdam polynomials (sometimes called Jacobi polynomials) P_λ(k) are orthogonal polynomials in several variables associated to root systems. They were introduced by .

They generalize Jack polynomials when the roots system is of type A, and are limits of Macdonald polynomials P_λ(q, t) as q tends to 1 and (1 - t)/(1 - q) tends to k.Main properties of the Heckman–Opdam polynomials have been detailed by Siddhartha Sahi ^[1]

Notes and References

1. A new formula for weight multiplicities and characters, Theorem 1.3. about Heckman–Opdam polynomials, Siddhartha Sahi