x CONTENT S 8.2. Ising , Potts, Vertex, Spin, and IRF models 7 9 8.3. Transfe r matrice s 8 2 8.4. Th e six-vertex model, Temperley-Lieb equivalenc e 8 3 8.5. Commutin g transfe r matrices , the Yang-Baxter equation 8 5 8.6. Verte x models on link diagrams 8 7 8.7. Spi n models on link diagrams 8 9 Lecture 9. Th e Algebraic Approach 9 3 9.1. Th e Hecke algebra 9 3 9.2. Th e relationship between the e, algebra and H(q, n) 9 4 9.3. Ocneanu' s trace on H(q, n) 9 5 9.4. Positivit y consideration s an d subfactor s fro m th e Hecke algebra 9 6 9.5. Th e Birman-Murakami-Wenzl algebr a 9 8 9.6. Th e Markov trace on the BMW algebra 10 0 9.7. Structur e o f the BMW algebra 10 1 9.8. Wenzl' s result on Brauer's centralizer algebr a 10 2 9.9. Quantu m invarian t theor y 10 3 Appendix 10 5 References 10 7
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