Volume 13, issue 2 (2009)

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Tutte chromatic identities from the Temperley–Lieb algebra

Paul Fendley and Vyacheslav Krushkal

Geometry & Topology 13 (2009) 709–741
Bibliography
1 D Bar-Natan, \ttdbnsymb (2008)
2 S. Beraha, Infinite nontrivial families of maps and chromials, PhD thesis, Johns Hopkins University (1975)
3 J S Birman, H Wenzl, Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313 (1989) 249 MR992598
4 B Bollobás, Modern graph theory, Graduate Texts in Math. 184, Springer (1998) MR1633290
5 P Fendley, Topological order from quantum loops and nets, Annals of Physics 323 (2008) 3113
6 P Fendley, V Krushkal, Link invariants, the chromatic polynomial and the Potts model arXiv:0806.3484
7 P Fendley, N Read, Exact $S$–matrices for supersymmetric sigma models and the Potts model, J. Phys. A 35 (2002) 10675 MR1959217
8 L. Fidkowski, M H. Freedman, C. Nayak, K. Walker, Z. Wang, From string nets to nonabelions arXiv:cond-mat/0610583
9 M H Freedman, A magnetic model with a possible Chern–Simons phase, Comm. Math. Phys. 234 (2003) 129 MR1961959
10 F Jaeger, On some graph invariants related to the Kauffman polynomial, from: "Progress in knot theory and related topics", Travaux en Cours 56, Hermann (1997) 69 MR1603130
11 V F R. Jones, Planar algebras arXiv:math/9909027
12 V F R Jones, Index for subfactors, Invent. Math. 72 (1983) 1 MR696688
13 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of $3$–manifolds, Annals of Math. Studies 134, Princeton University Press (1994) MR1280463
14 L Kauffmann, H Saleur, An algebraic approach to the planar coloring problem, Comm. Math. Phys. 152 (1993) 565 MR1213302
15 G Kuperberg, Spiders for rank $2$ Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
16 P Martin, D Woodcock, The partition algebras and a new deformation of the Schur algebras, J. Algebra 203 (1998) 91 MR1620713
17 E J Mlawer, S G Naculich, H A Riggs, H J Schnitzer, Group-level duality of WZW fusion coefficients and Chern–Simons link observables, Nuclear Phys. B 352 (1991) 863 MR1098252
18 J Murakami, The Kauffman polynomial of links and representation theory, Osaka J. Math. 24 (1987) 745 MR927059
19 R Penrose, Applications of negative dimensional tensors, from: "Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969)", Academic Press (1971) 221 MR0281657
20 H Saleur, Zeroes of chromatic polynomials: a new approach to Beraha conjecture using quantum groups, Comm. Math. Phys. 132 (1990) 657 MR1069841
21 H N V Temperley, E H Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the “percolation” problem, Proc. Roy. Soc. London Ser. A 322 (1971) 251 MR0498284
22 W T Tutte, More about chromatic polynomials and the golden ratio, from: "Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., 1969)", Gordon and Breach (1970) 439 MR0263698
23 W T Tutte, On chromatic polynomials and the golden ratio, J. Combinatorial Theory 9 (1970) 289 MR0272676
24 W T Tutte, Graph theory as I have known it, Oxford Lecture Ser. in Math. and its Appl. 11, The Clarendon Press, Oxford University Press (1998) MR1635397
25 K Walker, On Witten's $3$–manifold invariants
26 K Walker, Talk given at IPAM conference “Topological Quantum Computing”, (2007)
27 H Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 5 MR873400
28 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
29 S Yamada, An operator on regular isotopy invariants of link diagrams, Topology 28 (1989) 369 MR1014466