nLab
double Hecke algebra

Double Hecke algebras or Cherednik algebras. See also Calogero-Moser system and Dunkl operator.

• Pavel Etingof, Lectures on Calogero-Moser systems, pdf
• Ivan Cherednik, Introduction to double Hecke algebras, math.QA/0404307
• Yu. Berest, P. Etingof, V. Ginzburg, Finite-dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003, no. 19, 1053-1088.
• M. Haiman, Cherednik algebras, Macdonald polynomials and combinatorics, Proc. ICM, Madrid 2006, Vol. III, 843-872, djvu scan, author’s pdf
• P. Etingof, V. Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2) (2002) 243–348, MR2003b:16021, doi
• I. Cherednik, Double affine Hecke algebras. Knizhnik-Zamolodchikov equations, and Macdonald operators, IMRN (Duke Math. J.) 9 (1992), 171–180 MR1185831 (94b:17040), A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. math. 106 (1991), 411–431 MR1128220 (93b:17040)
• I. Cherednik, Y. Markov, Hankel transform via double Hecke algebra, math.QA/0004116
• Wee Liang Gan, Victor Ginzburg, Almost-commuting variety, $𝒟$-modules, and Cherednik algebras, With an appendix by Ginzburg. IMRP Int. Math. Res. Pap. 2006, 26439, 1–54, MR2008c:14062
• V. Ginzburg, N. Guay, E. Opdam, R. Rouquier, On the category $𝒪$ for rational Cherednik algebras, Invent. Math. 154 (3) (2003) 617–651
• Kevin McGerty, Microlocal KZ functors and rational Cherednik algebras, arxiv/1006.1599

There is also a $q$-deformation:

• Yuri Bazlov, Arkady Berenstein, Noncommutative Dunkl operators and braided Cherednik algebras, Selecta Math. (N.S.) 14 (2009), no. 3-4, 325–372, pdf, MR2010k:16044, doi