Hiroshima Mathematical Journal

Link invariant and $G_2$ web space

Takuro Sakamoto and Yasuyoshi Yonezawa

Full-text: Open access

Abstract

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.

Article information

Source
Hiroshima Math. J., Volume 47, Number 1 (2017), 19-41.

Dates
Received: 1 September 2015
Revised: 24 October 2016
First available in Project Euclid: 13 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1492048846

Digital Object Identifier
doi:10.32917/hmj/1492048846

Mathematical Reviews number (MathSciNet)
MR3634260

Zentralblatt MATH identifier
1366.81204

Subjects
Primary: 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Quantum link invariant Quantum group

Citation

Sakamoto, Takuro; Yonezawa, Yasuyoshi. Link invariant and $G_2$ web space. Hiroshima Math. J. 47 (2017), no. 1, 19--41. doi:10.32917/hmj/1492048846. https://projecteuclid.org/euclid.hmj/1492048846


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