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    Graphical Calculus for the Double Affine Q-Dependent Braid Group


    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:

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