Yokota type invariants derived from non-integral highest weight representations of q (s l 2)

Atsuhiko Mizusawa, Jun Murakami

    Research output: Contribution to journalArticle

    Abstract

    We define invariants for colored oriented spatial graphs by generalizing CM invariants [F. Costantino and J. Murakami, On SL(2,C) quantum 6j-symbols and their relation to the hyperbolic volume, Quantum Topol. 4 (2013) 303-351], which were defined via non-integral highest weight representations of q(sl2). We apply the same method used to define Yokota's invariants, and we call these invariants Yokota type invariants. Then, we propose a volume conjecture of the Yokota type invariants of plane graphs, which relates to volumes of hyperbolic polyhedra corresponding to the graphs, and check it numerically for some square pyramids and pentagonal pyramids.

    Original languageEnglish
    Article number1650054
    JournalJournal of Knot Theory and its Ramifications
    Volume25
    Issue number10
    DOIs
    Publication statusPublished - 2016 Sep 1

    Fingerprint

    Highest Weight Representations
    Invariant
    Square-based pyramid
    Hyperbolic Volume
    Spatial Graph
    Oriented Graph
    Plane Graph
    Pyramid
    Polyhedron
    Graph in graph theory

    Keywords

    • non-integral highest weight representation
    • spatial graph
    • Volume conjecture
    • Yokota's invariants

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Yokota type invariants derived from non-integral highest weight representations of q (s l 2). / Mizusawa, Atsuhiko; Murakami, Jun.

    In: Journal of Knot Theory and its Ramifications, Vol. 25, No. 10, 1650054, 01.09.2016.

    Research output: Contribution to journalArticle

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