Lecture Notes | Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Pavel Etingof

Departments

Mathematics

As Taught In

Fall 2009

Level

Graduate

Topics

Mathematics

Algebra and Number Theory

Linear Algebra

Topology and Geometry

Learning Resource Types

Lecture Notes

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Lecture Notes

Lecture notes on Cherednik Algebras

1. Introduction

2. Classical and quantum Olshanetsky-Perelomov systems for ﬁnite Coxeter groups

3. The rational Cherednik algebra

4. The Macdonald-Mehta integral

5. Parabolic induction and restriction functors for rational Cherednik algebras

6. The Knizhnik-Zamolodchikov functor

7. Rational Cherednik algebras and Hecke algebras for varieties with group actions

8. Symplectic reﬂection algebras

9. Calogero-Moser Spaces

10. Quantization of Claogero-Moser spaces

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