Double affine Hecke algebra

In mathematics, a double affine Hecke algebra, or Cherednik algebra, is an algebra containing the Hecke algebra of an affine Weyl group, given as the quotient of the group ring of a double affine braid group. They were introduced by Cherednik, who used them to prove Macdonald's constant term conjecture for Macdonald polynomials.

Definition

References

• Cherednik, Ivan (2005), Double affine Hecke algebras, London Mathematical Society Lecture Note Series, 319, Cambridge University Press, ISBN 978-0-521-60918-0, MR2133033 
• Haiman, Mark (2006), "Cherednik algebras, Macdonald polynomials and combinatorics", International Congress of Mathematicians. Vol. III, Eur. Math. Soc., Zürich, pp. 843–872, ISBN 978-3-03719-022-7, MR2275709, http://mathunion.org/ICM/ICM2006.3/ 
• A. A. Kirillov Lectures on affine Hecke algebras and Macdonald's conjectures Bull. Amer. Math. Soc. 34 (1997), 251–292.
• Macdonald, I. G. Affine Hecke algebras and orthogonal polynomials. Cambridge Tracts in Mathematics, 157. Cambridge University Press, Cambridge, 2003. x+175 pp. ISBN 0-521-82472-9 doi:10.2277/0521824729 MR2005b:33021