Abstract
Glen Burella (NUI Maynooth, Ireland)
Double Affine Hecke Algebra and nonsymmetric Macdonald polynomials
In this talk I will construct a double affine Hecke algebra starting with the well known braid group. I will discuss in detail its polynomial representation and explicitly derive the associated nonsymmetric Macdonald polynomials. Furthermore I will try to outline the connections of the representation theory of Lie Groups, Lie algebras and Kac-Moody algebras with the Hecke algebras and the Macdonald theory.