Macdonald–Koornwinder polynomials: where they came from and where they go to

Macdonald–Koornwinder polynomials (Contemp. Math. 138, 1992, pp. 189–204) are a five-paramter $q$-family of orthogonal polynomials in n variables attached to root system $BC_n$. They are a common generalization of $BC_n$ type Macdonald polynomials and Askey–Wilson polynomials. The lecture will discuss developments since 1970 leading to these polynomials and some of their impact after they were introduced.

References

1. Tom H. Koornwinder, “Askey–Wilson polynomials for root systems of type $BC$.”, Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991), Contemp. Math., 138, Amer. Math. Soc., Providence, RI, 1992, 189–204