The quantum G_2 link invariant

Details The quantum G_2 link invariant The quantum G_2 link invariant

1991-10-07

arxiv.org/abs/math/9201302v1

Internat. J. Math. 5 (1994), no. 1, 61--85

Mathematics

Quantum Algebra

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Scientific paper

We derive an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant of links and tangled graphs. We show that the invariant equals the Reshetikhin-Turaev invariant corresponding to the exceptional simple Lie algebra G_2. It is therefore related to G_2 in the same way that the HOMFLY polynomial is related to A_n and the Kauffman polynomial is related to B_n, C_n, and D_n. We give parallel constructions for the other rank 2 Lie algebras and present some combinatorial conjectures motivated by the new inductive definitions.

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