Required Readings

In order to prepare for class, students are required to read selections from the course notes. These readings can be found on the lecture notes page.

1 Classical and quantum Olshanetsky-Perelomov systems for finite Coxeter groups Chapter 2
2 The rational Cherednik algebra I Chapter 3, sections 3.1-3.13

The rational Cherednik algebra II

Finite Coxeter groups and the Macdonald-Mehta integral

Chapter 3, sections 3.14-3.17

Chapter 4, section 4.1

4 The Macdonald-Mehta integral Chapter 4, sections 4.2-4.4
5 Parabolic induction and restriction functors for rational Cherednik algebras Chapter 5

The Knizknik-Zamolodchikov functor

Rational Cherednik algebras for varieties with group actions

Chapter 6

Chapter 7, sections 7.1-7.5

7 Hecke algebras for varieties with group actions Chapter 7, sections 7.6-7.15
8 Symplectic reflection algebras I Chapter 8, sections 8.1-8.7
9 Symplectic reflection algebras II Chapter 8, sections 8.8-8.13
10 Calogero-Moser spaces Chapter 9
11 Quantization of Calogero-Moser spaces Chapter 10

Supplemental Readings

Bezrukavnikov, R., and P. Etingof. “Parabolic Induction and Restriction Functors for Rational Cherednik Algebras.” Selecta Math 14, nos. 3-5 (2009): 397-425.

Etingof, P., and V. Ginzburg. “Symplectic Reflection Algebras, Calogero-Moser Space, and Deformed Harish-Chandra Homomorphism.” arXiv:math/0011114.

Rouquier, R. “Representations of Rational Cherednik Algebras.” arXiv:math/0504600.

Etingof, P. Lectures on Calogero-Moser Systems. arXiv:math/0606233.

———. “Cherednik and Hecke Algebras of Varieties With a Finite Group Action.” arXiv: math.QA/0406499.

———. “A Uniform Proof of the Macdonald-Mehta-Opdam Identity for Finite Coxeter Groups.” arXiv:0903.5084.

———. “Supports of Irreducible Spherical Representations of Rational Cherednik Algebras of Finite Coxeter Groups.” arXiv:0911.3208.

Course Info

As Taught In
Fall 2009