Graphical Calculus for the Double Affine Q-Dependent Braid Group
Mathematical Physics
2015-06-16 v1 math.MP
Abstract
We define a double affine -dependent braid group. This group is constructed by appending to the braid group a set of operators , before extending it to an affine -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 -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 upon which this algebra is dependent and show that in this particular representation corresponds to a twist in the ribbon.
Cite
@article{arxiv.1307.4227,
title = {Graphical Calculus for the Double Affine Q-Dependent Braid Group},
author = {Glen Burella and Paul Watts and Vincent Pasquier and Jiri Vala},
journal= {arXiv preprint arXiv:1307.4227},
year = {2015}
}