Hecke algebras, modular categories and 3-manifolds quantum invariants

Topology

Volumn 39, Issue 1, 2000, Pages 193-223

  Blanchet, Christian ^a  

^a UNIVERSITÉ DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033633809     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-9383(98)00066-4     Document Type: Article

References (42)

1. A.K. Aiston, Skein Theoretic Idempotents of Hecke Algebras and Quantum Group Invariants. Thesis, University of Liverpool, 1996.
2. A.K. Aiston, A Skein Theoretic Proof of The Hook Formula for Quantum Dimension. Preprint, 1997.
3. A.K. Aiston, H.R. Morton, Idempotents of hecke algebras of type A, Journal of Knot Theory and Ramifications 7(4) (1998) 463-487.
4. H.H. Andersen, Tensor products of quantized tilting modules, Communication in Mathematical Physics 149 (1991) 149-159.
5. C. Blanchet, Invariants on three-manifolds with spin stucture, Commentarii Mathematici Helvetici 67 (1992) 406-427.
6. C. Blanchet, Refined quantum invariants for three-manifolds with structure. In: Knot Theory, Banach Center Publication Vol. 42, 1998, pp. 11-22.
7. C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34(4) (1995) 883-927.
8. N. Bourbaki, Groupes et Algèbrès De Lie IV,V,VI. Masson, Paris, 1982.
9. N,q. Preprint, 1998.
10. A. Bruguières, Catégories Prémodulaires, Modularisations, Et Invariants Des Variétés De Dimension 3. Preprint, 1998.
11. G. Dipper, G. James, Block idempotents of the hecke algebra of the general linear group, Proceedings of The London Mathematical Society 54 (1987) 57-82.
12. J. Erlijman, New subfactors from braid group representations, Transactions of The American Mathematical Society 350(1) (1998), 185-211.
13. M. Geck, Representations of hecke algebras at roots of unity. Séminaire Bourbaki No 836, November 1997.
14. F.M. Goodman, H. Wenzl, Littlewood-Richardson coefficients for hecke algebras at roots of unity, Advances in Mathematics 82 (1990) 244-265.
15. A. Gyoja, A q-analogue of young symmetrizer, Osaka Journal of Mathematics 23 (1986) 841-852.
16. P. Freyd, D. Yetter, J. Hoste, W.B.R. Lickorish, K. Millet, A. Ocneanu, A new polynomial invariant of knots and links, Bulletin of the AMS 12 (1985) 239-246.
17. V. Jones, Hecke algebra representations of braid groups and link polynomials, Annals of Mathematics 126 (1987) 335-338.
18. D. Kazhdan, H. Wenzl, Reconstructing monoidal categories, Advances in Soviet Mathematics 16(2) (1993) 111-136.
19. 3, Inventiones Mathematicae 45 (1978) 35-56.
20. R. Kirby, P. Melvin, The 3-manifold invariants of witten and reshetikhin-turaev for sl(2, C), Inventiones Mathematicae 105 (1991) 473-545.
21. T. Kohno, T. Takata, Symmetry for witten's 3-manifold invariants for sl(n, C), Journal of Knot Theory and Ramifications 2 (1993) 149-169.
22. T. Kohno, T. Takata, Level-rank duality for witten's 3-manifold invariant, advanced studies in pure mathematics 24, Progress in Algebraic Combinatorics, 243-264.
23. W.B.R. Lickorish, Sampling the SU(N) invariants of three-manifolds, Journal of Knot Theory and Ramifications (1997).
24. B.W.R. Lickorish, Skeins, SU(N) Three-manifolds Invariants and TQFT. Preprint, 1997.
25. I.G. Macdonald, Symmetric functions and hall polynomials. Oxford Mathematics Monographs, 1979.
26. G. Masbaum, H. Wenzl, Integral modular categories and integrality of quantum invariants at roots of unity of prime order, Journal Fur Die Reine Und Angewandte Mathematik 505 (1998) 209-235
27. H.R. Morton, Invariants of links and 3-manifolds from skein theory and from quantum groups. In Topics in Knot Theory, N.A.T.O. A.S.I. Series C 399. ed. M. Bozhyk, Kluwer, 1993, pp. 107-156.
28. H.R. Morton, A.K. Aiston, Young diagrams, the homfly skein of the annulus and unitary invariants. In Proceedings of Knots 96, ed. Shin'ichi Suzuki. World Scientific, Singapore, 1997, pp. 31-45.
29. H.R. Morton, P. Traczyk, Knots and algebras, Contribuciones Matematicas en Homaje al Professor D. Antonio Plans Sanz de Bremond, E. Martin-Peinador and A. Rodez editors, University of Saragoza, 1990, pp. 201-220.
30. H. Murakami, Quantum invariants for 3- Manifolds, Proceedings of The 3rd Korea-Japan School of Knots and Links.
31. H. Murakami, T. Othsuki, M. Okada, Invariants of three-manifolds derived from linking matrices of framed links, Osaka Journal of Mathematics 29 (1992) 545-572.
32. J. Przytycki, P. Traczyk, Invariants of links of conway type, Kobe Journal of Mathematics 4 (1987) 115-139.
33. A. Ram, H., Wenzl, Matrix units for centralizer algebras, Journal of Algebra 145 (1992) 378-395.
34. N. Reshetikhin, V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Inventiones Mathematicae 103 (1991) 547-598.
35. V.G. Turaev, Operator invariants of tangles, and R-matrices, Math. USSR Izv. 35(2) (1990) 411-443.
36. V.G. Turaev, Quantum invariants of knots and 3-manifolds, De Gruyter Studies in Mathematics 18 (1994).
37. V. Turaev, H. Wenzl, Quantum invariants of 3-manifolds associated with classical simple lie algebras, International Journal of Mathematics 4(2) (1993) 323-358.
38. V. Turaev, H. Wenzl, Semisimple and modular categories from link invariants, Mathematische Annalen 309 (1997) 411-461.
39. P. Vogel, Les invariants récents des variétés de dimension 3. Séminaire Bourbaki, 1995, 799.
40. n and subfactors, Inventiones Mathematicae 92 (1998) 349-383.
41. H. Wenzl, Braids and invariants of 3-manifolds, Inventiones Mathematicae 114 (1993) 235-275.
42. Y. Yokota, Skeins and quantum SU(N) invariants of 3-manifolds, Mathematische Annalen 307 (1997) 109-138.