Topic #9 --------------- OP-SF NET --------------- February 9, 1995 ~~~~~~~~~ From: OP-SF Net Editor Subject: Lecture Notes on Affine Hecke algebras and Macdonald conjectures The following lecture notes are available as file hecke.tex from Waleed Al-Salam's anonymous ftp site: Alexander A. Kirillov. Jr., Lectures on the affine Hecke algebras and Macdonald conjectures, These are the notes from a series of lectures the author gave at Harvard University in the Fall of 1994. The goal of these lectures is to give a self-contained exposition of a recent result of I. Cherednik, who proved I.G. Macdonald's inner product conjectures for arbitrary root systems, using the algebraic structure he called "double affine Hecke algebra". In order to make these lectures understandable to a general mathematical audience, the author gives all necessary definitions (including that of Macdonald's polynomials, Hecke algebras, etc.) and motivations in the course. However, familiarity with (finite-dimensional and affine) root systems and Weyl groups is assumed. The author gives much credit to earlier lecture courses on the subject by Ivan Cherednik, Howard Garland and Ian Macdonald.