Plamen Iliev (Georgia Institute of Technology, Atlanta, USA)

A Lie theoretic interpretation of multivariate hypergeometric polynomials

Abstract:
   In 1971 Griffiths defined polynomials in d-variables orthogonal with respect to the multinomial distribution. The polynomials possess an interesting duality between the discrete variables and the degree indices. In my talk, I will give an interpretation of these polynomials within the context of the Lie algebra sl_d+1. In particular, this approach shows that the polynomials diagonalize two commutative algebras of partial difference operators: one acting on the variables of the polynomials, and the other one on their degree indices.