Graphical Calculus for the Double Affine Q-Dependent Braid Group


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:

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