Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics

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)

MIT Course Number

18.735

As Taught In

Fall 2009

Level

Graduate

Cite This Course

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.

Etingof, Pavel. 18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics, Fall 2009. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-735-double-affine-hecke-algebras-in-representation-theory-combinatorics-geometry-and-mathematical-physics-fall-2009 (Accessed). License: Creative Commons BY-NC-SA


For more information about using these materials and the Creative Commons license, see our Terms of Use.


Close