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arXiv · 0908.0542

Integrality of Kauffman brackets of trivalent graphs

Francesco Costantino
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Abstract

We show that Kauffman brackets of colored framed graphs (also known as quantum spin networks) can be renormalized to a Laurent polynomial with integer coefficients by multiplying it by a coefficient which is a product of quantum factorials depending only on the abstract combinatorial structure of the graph. Then we compare the shadow-state sums and the state-sums based on $R$-matrices and Clebsch-Gordan symbols, reprove their equivalence and comment on the integrality of the weight of the states. We also provide short proofs of most of the standard identities satisfied by quantum $6j$-symbols of $U_q(sl_2)$.

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Francesco Costantino. 2009-11-29. Integrality of Kauffman brackets of trivalent graphs. https://arxiv.org/abs/0908.0542

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