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. Infinitesimal Cherednik algebras have significant implications in representation theory, and therefore have important applications in particle physics and in chemistry.

References

• Cherednik, Ivan (2005), Double affine Hecke algebras, London Mathematical Society Lecture Note Series, 319, Cambridge University Press, ISBN 978-0-521-60918-0, MR 2133033
• 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, MR 2275709, archived from the original on 2011-08-20, retrieved 2011-06-09
• 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 MR1976581