nLab Ivan Cherednik

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Selected writings

On the Knizhnik-Zamolodchikov equation and Hecke algebras:

• Ivan Cherednik, Lectures on Knizhnik-Zamolodchikov equations and Hecke algebras, Mathematical Society of Japan Memoirs 1998 (1998) 1–96 $[$doi:10.2969/msjmemoirs/00101C010$]$

Cherednik introduced the reflection equation in the context of quantum inverse scattering method with boundary conditions:

• I. V. Cherednik: Factorizing particles on a half-line and root systems, Theoretical and Mathematical Physics 61 (1984) 977-983 [doi:10.1007/BF01038545, doi:10.1007/BF01038545]

Double Hecke algebras are also called Cherednik algebras, after I. Cherednik who introduced in a series of works in early 1990s:

• Ivan 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); Double affine Hecke algebras and Macdonald’s conjectures, Ann. of Math.(2) 141:1 (1995) 191–216.

A monograph on this subject is

• Ivan Cherednik, Double affine Hecke algebras, London Math. Soc. Lecture Note Series 319, Cambridge Univ. Press 2005

An introduction into the monograph above is the preprint

• Ivan Cherednik, Introduction to double Hecke algebras, math.QA/0404307
• Ivan Cherednik, Y. Markov, Hankel transform via double Hecke algebra, math.QA/0004116

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