![Four relations: s^2=1, sx=-xs, sy=ys, and [y,x] = t-2cs.](/courses/mathematics/18-735-double-affine-hecke-algebras-in-representation-theory-combinatorics-geometry-and-mathematical-physics-fall-2009/18-735f09.jpg "Four relations: s^2=1, sx=-xs, sy=ys, and [y,x] = t-2cs.")
The four relations that define the simplest Cherednik algebra. (Image by MIT OpenCourseWare.)
Instructor(s)
Prof. Pavel Etingof
MIT Course Number
18.735
As Taught In
Fall 2009
Level
Graduate
Course Description
Course Features
Course Description
Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.