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    Representation Theory of Categorified Quantum sl2

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    Chatav_grad.sunysb_0771E_11132.pdf (487.0Kb)
    Date
    1-Aug-12
    Author
    Chatav, Eitan
    Publisher
    The Graduate School, Stony Brook University: Stony Brook, NY.
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    Abstract
    Quantum sl2 gives rise to the Jones polynomial knot invariant. One of the insights of categorification is that this 3-dimensional picture is a shadow, the decategorification, of a 4-dimensional picture. Thus, the categorification of quantum sl2 gives rise through its representation theory to Khovanov homology, the categorification of the Jones polynomial. In the 3-dimensional picture, the algebra of Temperley-Lieb diagrams, used in the construction of the Jones polynomial, gives a graphical calculus for intertwiners of the representations of quantum sl2. We show that the algebra of Bar-Natan's dotted cobordisms, used in the construction of Khovanov homology, gives a graphical calculus for intertwiners of representations of categorified quantum sl2.
    Description
    54 pg.
    URI
    http://hdl.handle.net/1951/59604
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    • Stony Brook Theses & Dissertations [SBU] [1955]

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