## Hiroshima Mathematical Journal

### Link invariant and $G_2$ web space

#### 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
Revised: 24 October 2016
First available in Project Euclid: 13 April 2017

https://projecteuclid.org/euclid.hmj/1492048846

Digital Object Identifier
doi:10.32917/hmj/1492048846

Mathematical Reviews number (MathSciNet)
MR3634260

Zentralblatt MATH identifier
1366.81204

#### 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