MURAL - Maynooth University Research Archive Library

    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.

    [img] Download (1MB)

    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...

    Add this article to your Mendeley library


    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
    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

    Repository Staff Only(login required)

    View Item Item control page


    Downloads per month over past year

    Origin of downloads