Graphical Calculus for the Double Affine QDependent Braid Group
Abstract
We define a double affine $Q$dependent braid group. This group is constructed by appending to the braid group a set of operators $Q_i$, before extending it to an affine $Q$dependent braid group. We show specifically that the elliptic braid group and the double affine Hecke algebra (DAHA) can be obtained as quotient groups. Complementing this we present a pictorial representation of the double affine $Q$dependent braid group based on ribbons living in a toroid. We show that in this pictorial representation we can fully describe any DAHA. Specifically, we graphically describe the parameter $q$ upon which this algebra is dependent and show that in this particular representation $q$ corresponds to a twist in the ribbon.
 Publication:

Annales Henri Poincaré
 Pub Date:
 November 2014
 DOI:
 10.1007/s000230130289x
 arXiv:
 arXiv:1307.4227
 Bibcode:
 2014AnHP...15.2177B
 Keywords:

 Mathematical Physics
 EPrint:
 doi:10.1007/s000230130289x