Okounkov's BC-type interpolation Macdonald polynomials and their q=1 limit

Understand

This paper surveys eight classes of polynomials associated with $A$-type and $BC$-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and Macdonald polynomials and their $BC$-type extensions.

• Among these the $BC$-type interpolation Jack polynomials were probably unobserved until now.
• Much emphasis is put on combinatorial formulas and binomial formulas for (most of) these polynomials.
• Possibly new results derived from these formulas are a limit from Koornwinder to Macdonald polynomials, an explicit formula for Koornwinder polynomials in two variables, and a combinatorial expression for the coefficients of the expansion of $BC$-type Jacobi polynomials in terms of Jack polynomials which is different from Macdonald's combinatorial expression.