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.
| WEEK # | TOPICS | READINGS |
|---|---|---|
| 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 |
| 3 |
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 |
| 6 |
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.