Link invariant and $G_2$ web space

Other literature type English OPEN
Sakamoto, Takuro ; Yonezawa, Yasuyoshi (2017)
  • Publisher: Hiroshima University, Department of Mathematics
  • Journal: (issn: 0018-2079)
  • Subject: Quantum group | 81R50 | Quantum link invariant | 57M25
    arxiv: Computer Science::Information Retrieval | Computer Science::Digital Libraries | Mathematics::Geometric Topology | Mathematics::Quantum Algebra

In this paper, we reconstruct Kuperberg’s $G_2$ web space [5, 6]. We introduce a new web diagram (a trivalent graph with only double edges) and new relations between Kuperberg’s web diagrams and the new web diagram. Using the web diagrams, we give crossing formulas for the $R$-matrices associated to some irreducible representations of $U_q(G_2)$ and calculate $G_2$ quantum link invariants for generalized twist links.
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