nLab rational Cherednik algebra

Idea

Rational Cherednik algebras are certain degenerations of double affine Hecke algebras.

Literature

• Yu. Berest, P. Etingof, V. Ginzburg, Finite-dimensional representations of rational Cherednik algebras, Int. Math. Res. Not. 2003, no. 19, 1053–1088.

• V. Ginzburg, N. Guay, E. Opdam, R. Rouquier, On the category $\mathcal{O}$ for rational Cherednik algebras, Invent. Math. 154 (3) (2003) 617–651

• Kevin McGerty, Microlocal KZ functors and rational Cherednik algebras, arxiv:1006.1599

• Pavel Etingof, Victor Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2) (2002) 243–348, MR2003b:16021, doi

• Y. Bazlov, A. Berenstein, E. Jones-Healey, A. McGaw, Twists of rational Cherednik algebras, arXiv:2205.11971

There is also a braided/$q$-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

category: algebra