Lecture notes on Cherednik algebras

Abstract

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.

92 pages, latex; misprints corrected and references added in the revised version

References in corpus (2)

• Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups
• Reflection Groups. A Contribution to the Handbook of Algebra

Cited by in corpus (23)

• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• The spherical sector of the Calogero model as a reduced matrix model
• Representations of Rational Cherednik Algebras in Positive Characteristic
• Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
• Matrix addition and the Dunkl transform at high temperature
• Geometric representations of graded and rational Cherednik algebras
• Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p
• Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups
• The combinatorics of ${\mathbb{C}}^{\ast }$-fixed points in generalized Calogero-Moser spaces and Hilbert schemes
• Elliptic and $q$-Analogs of the Fibonomial Numbers
• On representations of rational Cherednik algebras in complex rank
• The Hilbert Series of the Irreducible Quotient of the Polynomial Representation of the Rational Cherednik Algebra of Type $A_{n-1}$ in Characteristic $p$ for $p|n-1$
• Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic
• Arc spaces and DAHA representations
• An exceptional symmetry algebra for the 3D Dirac-Dunkl operator
• Exterior powers of the reflection representation in Springer theory
• Category O for the rational Cherednik algebra associated to the complex reflection group G_12
• Deformations of unitary Howe dual pairs
• Knizhnik--Zamolodchikov functor for degenerate double affine Hecke algebras : algebraic theory
• The Rational Cherednik Algebra of Type $A_1$ with Divided Powers
• Quasi-Invariants in Characteristic $p$ and Twisted Quasi-Invariants
• Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System
• The Dunkl-Cherednik Deformation of a Howe duality