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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 (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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