Burella, Glen and Watts, Paul and Pasquier, Vincent and Vala, Jiri (2013) Graphical Calculus for the Double Affine Q-Dependent Braid Group. Working Paper. arXiv.org.

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Abstract

We define a double affine Q-dependent braid group. This group is constructed by appending to the braid group a set of operators Qi, before extending it to an affine Q-dependent braid group. We show specifically 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. Specifically, 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.

Item Type:	Monograph (Working Paper)
Additional Information:	Cite as: arXiv:1307.4227 [math-ph]
Keywords:	Graphical Calculus; Double Affine; Q-Dependen;t Braid Group; DAHA;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	4501
Depositing User:	Dr. Jiri Vala
Date Deposited:	17 Sep 2013 15:40
Publisher:	arXiv.org
URI:	http://arxiv-web3.library.cornell.edu/ab...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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