Arun Ram, part2 "Generalised divided differences and Monk rules"

Abstract: Generalised divided differences are a tool for building Macdonald polynomials, analogous to the way that classical divided differences are a tool for building Schubert polynomials. The calculus of generalised divided differences is called the double affine Hecke algebra, analogous to the way that the calculus of classical divided differences is called the nil Hecke algebra. In the first half of the talk I will review the analogies. In the second half I will explain how we use the calculus of generalised divided differences to compute Monk rules for Macdonald polynomials (joint work with Tom Halverson).