• Corpus ID: 115173974

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. 
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References

SHOWING 1-10 OF 83 REFERENCES
On some representations of the rational Cherednik algebra Represent
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
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
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
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
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
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
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
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
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
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…
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