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March 2017 Link invariant and $G_2$ web space
Takuro Sakamoto, Yasuyoshi Yonezawa
Hiroshima Math. J. 47(1): 19-41 (March 2017). DOI: 10.32917/hmj/1492048846

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.

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Takuro Sakamoto. Yasuyoshi Yonezawa. "Link invariant and $G_2$ web space." Hiroshima Math. J. 47 (1) 19 - 41, March 2017. https://doi.org/10.32917/hmj/1492048846

Information

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

zbMATH: 1366.81204
MathSciNet: MR3634260
Digital Object Identifier: 10.32917/hmj/1492048846

Subjects:
Primary: 81R50
Secondary: 57M25

Rights: Copyright © 2017 Hiroshima University, Mathematics Program

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Vol.47 • No. 1 • March 2017
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