SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

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.

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