Lecture notes on Cherednik algebras

2010/01/04 by Pavel Etingof, Etingof, Pavel, Xiaoguang Ma +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1001.0432

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

openalex publication_date 2010/01/04 · arxiv created 2010/04/19 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Reflection Groups. A Contribution to the Handbook of Algebra
• Algebraic Families on an Algebraic Surface
• Differential-difference operators associated to reflection groups
• Lectures on Calogero-Moser systems
• Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups

Cited by

• Explicit Computations for the Classical and Quantum Integrability of the 3-Dimensional Rational Calogero-Moser System
• Gaussian integrals on symmetric spaces (the complex case and beyond)

Related

• A Course of Algebra (PART I)
• Lecture notes on operator algebras and their application in physics
• Notes on C^*-algebras
• Lectures on the affine Hecke algebras and Macdonald conjectures
• Notes on Siegfried Bosch's Algebraic Geometry and Commutative Algebra (dedicated to Grothendieck)