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Last updated:

November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Double affine Hecke algebras (DAHA)

also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems

Course Curriculum

  • Introduction Unlimited
  • Classical and quantum Olshanetsky-Perelomov systems for finite Coxeter groups Unlimited
  • The rational Cherednik algebra Unlimited
  • The Macdonald-Mehta integral Unlimited
  • Parabolic induction and restriction functors for rational Cherednik algebras Unlimited
  • The Knizhnik-Zamolodchikov functor Unlimited
  • Rational Cherednik algebras and Hecke algebras for varieties with group actions Unlimited
  • Symplectic reflection algebras Unlimited
  • Calogero-Moser spaces Unlimited
  • Quantization of Calogero-Moser spaces Unlimited

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Massachusetts Institute of Technology