MIT Combinatorics Seminar

BC_n-symmetric polynomials

Eric Rains  (UC Davis)

Wednesday, November 24, 2004    4:15 pm    Room 2-338


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)