I'll discuss two families of Laurent polynomials with hyperoctahedral
symmetry, both indexed by partitions. The first, Koornwinder's
orthogonal polynomials, includes all of the classical (and quantum
classical) spherical functions and characters as special and limiting
cases, as well as the Jack and Macdonald polyomials. The second,
Okounkov's interpolation polynomials, is defined (and overdetermined) by
specifying a large collection of zeros. Despite the significant
differences in definitions, these two families are in fact closely
related. I'll discuss this connection, and show how it leads to new
proofs of the known properties of Koornwinder polynomials, as well as
proofs of properties not previously discovered.
(joint talk with Lie Groups Seminar)