# Lecture notes on Cherednik algebras

@article{Etingof2010LectureNO, title={Lecture notes on Cherednik algebras}, author={Pavel Etingof and Xiaoguang Ma}, journal={arXiv: Representation Theory}, year={2010} }

The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other mathematical objects.

## 44 Citations

Symplectic reflection algebras

- Mathematics
- 2012

These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to…

Rational Cherednik Algebras

- Mathematics
- 2011

We survey a number of results about the rational Cherednik algebra’s representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification…

Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic

- Mathematics
- 2012

We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded…

Category O for the rational Cherednik algebra associated to the complex reflection group G 12

- Mathematics
- 2010

The polynomial representation of the type An−1 rational Cherednik algebra in characteristic p | n

- Mathematics
- 2015

ABSTRACT We study the polynomial representation of the rational Cherednik algebra of type An−1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the…

Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010

- Mathematics
- 2010

We survey a number of results about the rational Cherednik algebra’s representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification…

Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H_3

- Mathematics
- 2010

New realizations of deformed double current algebras and Deligne categories

- Mathematics
- 2020

In this paper we propose an alternative construction of a certain class of Deformed Double Current Algebras. We construct them as spherical subalgebras of symplectic reflection algebras in the…

## References

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On some representations of the rational Cherednik algebra Represent

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We study lowest weight representations of the rational Cherednik algebra attached to a complex reflection group W. In particular, we generalize a number of previous results due to Berest, Etingof,…

Lectures on Calogero-Moser systems

- Mathematics
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These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.

Finite-dimensional representations of rational Cherednik algebras

- Mathematics
- 2002

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are…

Reflection Groups. A Contribution to the Handbook of Algebra

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- 2003

This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.

On the category 𝒪 for rational Cherednik algebras

- Mathematics
- 2002

Abstract We study the category 𝒪 of representations of the rational Cherednik algebra AW attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov…

On the Cohomology Ring of an Algebra

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We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some…

Poincaré–Birkhoff–Witt Theorem for Quadratic Algebras of Koszul Type

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Abstract In this paper we prove a general Poincare–Birkhoff–Witt theorem for quadratic Koszul algebras. The result is similar to that obtained by Polischuk and Positselsky, but the proof is entirely…

Almost-commuting variety, D-modules, and Cherednik algebras

- Mathematics
- 2004

We study a scheme M closely related to the set of pairs of n by n-matrices with rank 1 commutator. We show that M is a reduced complete intersection with n+1 irreducible components, which we…

Cherednik and Hecke algebras of varieties with a finite group action

- Mathematics
- 2004

This paper is an expanded and updated version of the preprint arXiv:math/0406499. It includes a more detailed description of the basics of the theory of Cherednik and Hecke algebras of varieties…

Parabolic induction and restriction functors for rational Cherednik algebras

- Mathematics
- 2008

Abstract.We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation…