Double affine Hecke algebra
Encyclopedia
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 polynomial
s.
Hecke algebra
In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a one-parameter deformation of the group algebra of a Coxeter group....
of an affine Weyl group, given as the quotient of the group ring of a double affine braid group
Double affine braid group
In mathematics, a double affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double affine Hecke algebras in the same way that the group rings of affine braid groups have quotients that are affine Hecke algebras.For affine An...
. They were introduced by Cherednik, who used them to prove Macdonald's constant term conjecture for Macdonald polynomial
Macdonald polynomial
In mathematics, Macdonald polynomials Pλ are a family of orthogonal polynomials in several variables, introduced by...
s.