Burella, Glen and Watts, Paul and Pasquier, Vincent and Vala, Jiri (2014) Graphical Calculus for the Double Affine Q-Dependent Braid Group. Annales Henri Poincare, 15. pp. 2177-2201. ISSN 1424-0637

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Abstract

In this paper, we present a straightforward pictorial representation of the double affine Hecke algebra (DAHA) which enables us to translate the abstract algebraic structure of a DAHA into an intuitive graphical calculus suitable for a physics audience. Initially, we define the larger 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 specifically that the elliptic braid group and the 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.

Item Type:	Article
Additional Information:	The definitive version of this article is available at DOI 10.1007/s00023-013-0289-x
Keywords:	Graphical Calculus; Double Affine Q-Dependent Braid Group;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	5564
Identification Number:	https://doi.org/10.1007/s00023-013-0289-x
Depositing User:	Dr. Jiri Vala
Date Deposited:	19 Nov 2014 16:02
Journal or Publication Title:	Annales Henri Poincare
Publisher:	Springer Verlag
Refereed:	Yes
URI:	http://link.springer.com/journal/23
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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