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 A_n groups, the double affine braid group is the fundamental group of the space of n distinct points on a 2-dimensional torus.

References

• Haiman, Mark (2006). "Cherednik algebras, Macdonald polynomials and combinatorics". International Congress of Mathematicians 3. Eur. Math. Soc., Zürich. pp. 843–872. ISBN 978-3-03719-022-7. MR 2275709 
• Macdonald, I. G. (2003). Affine Hecke Algebras and Orthogonal Polynomials. Cambridge University Press. doi:10.2277/0521824729. ISBN 0-521-82472-9. MR 2005b:33021.