publication . Preprint . Article . Other literature type . 2017

Linv invariant and $G_2$ web space

Takuro Sakamoto; Yasuyoshi Yonezawa;
Open Access English
  • Published: 01 Mar 2017
Abstract
In this paper, we reconstruct Kuperberg's $G_2$ web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the $G_2$ webs, we define crossing formulas corresponding to R-matrices associated to some $G_2$ irreducible representations and calculate $G_2$ quantum link invariant for some torus links.
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Subjects
arXiv: Mathematics::Geometric TopologyMathematics::Differential GeometryComputer Science::Information RetrievalComputer Science::Digital LibrariesMathematics::Quantum Algebra
free text keywords: Mathematics - Geometric Topology, Mathematics - Quantum Algebra, Quantum link invariant, 81R50, 57M25, Mathematics, Quantum group, Diagram, Invariant (mathematics), Discrete mathematics, Quantum, Web space, Torus, Irreducible representation

[1] V. G. Drinfel'd, Quantum groups, In Proceedings of the International Congress of Mathematicians, Berkeley, California, 798-820, (1987)

[2] J, Huang and C. Zhu, Weyl's construction and tensor power decomposition for G2. Proc. Amer. Math. Soc. 127 (1999), 925-934.

[3] M. Jimbo, A q-difference analogue of Uq(g) and the Yang-Baxter equation, Lett. Math. Phys. 10, 63-69,(1985)

[4] L. H. Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990), 417-471. [OpenAIRE]

[5] G. Kuperberg, The quantum G2 link invariant, International Journal of Mathematics, Volume 5, No.1(1994), 61-85

[6] G. Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. , Volume 180, 109-151, (1996) [OpenAIRE]

[7] G. I. Lehrer and R.B. Zhang, Strongly multiplicity free modules for Lie algebras and quantum groups. J. Algebra 306 (2006), 138-174. [OpenAIRE]

[8] S. Morrison, E. Peters and N. Snyder, Knot polynomial identities and quantum group coincidences. Quantum Topol. 2 (2011), 101-156.

[9] N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. , Volume 127, Number 1(1990), 1-26 [OpenAIRE]

[10] T. Sakamoto, Link invariant of G2 quantum group and fundamental representations (in Japanese), Master thesis, Nagoya University, (2015)

[11] G.E. Schwarz, Invariant theory of G2 and Spin7, Comment. Math. Helv. 63 (1988), 624-663.

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