Project Euclid

References

• [BLM] A. Beĭ linson, G. Lusztig, and R. MacPherson, A geometric setting for the quantum deformation of $\rm GL\sb n$, Duke Math. J. 61 (1990), no. 2, 655–677.
  Mathematical Reviews (MathSciNet): MR91m:17012
  Zentralblatt MATH: 0713.17012
  Digital Object Identifier: doi:10.1215/S0012-7094-90-06124-1
  Project Euclid: euclid.dmj/1077296831
  
• [CF] L. Crane and I. B. Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35 (1994), no. 10, 5136–5154.
  Mathematical Reviews (MathSciNet): MR96d:57019
  Zentralblatt MATH: 0892.57014
  Digital Object Identifier: doi:10.1063/1.530746
  
• [D] V. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798–820.
  Mathematical Reviews (MathSciNet): MR89f:17017
  Zentralblatt MATH: 0667.16003
  
• [GK] V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994), no. 1, 203–272.
  Mathematical Reviews (MathSciNet): MR96a:18004
  Zentralblatt MATH: 0855.18006
  Digital Object Identifier: doi:10.1215/S0012-7094-94-07608-4
  Project Euclid: euclid.dmj/1077286744
  
• [J] M. Jimbo, A $q$-analogue of $U(\germ g\germ l(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252.
  Mathematical Reviews (MathSciNet): MR87k:17011
  Zentralblatt MATH: 0602.17005
  Digital Object Identifier: doi:10.1007/BF00400222
  
• [Ks] M. Kashiwara, On crystal bases of the $Q$-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465–516.
  Mathematical Reviews (MathSciNet): MR93b:17045
  Zentralblatt MATH: 0739.17005
  Digital Object Identifier: doi:10.1215/S0012-7094-91-06321-0
  Project Euclid: euclid.dmj/1077295931
  
• [KL] L. H. Kauffman and S. L. Lins, Temperley-Lieb recoupling theory and invariants of $3$-manifolds, Annals of Mathematics Studies, vol. 134, Princeton University Press, Princeton, NJ, 1994.
  Mathematical Reviews (MathSciNet): MR95c:57027
  Zentralblatt MATH: 0821.57003
  
• [KR] A. N. Kirillov and N. Y. Reshetikhin, Representations of the algebra $U\sb q(\rm sl(2)),\;q$-orthogonal polynomials and invariants of links, Infinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988), Adv. Ser. Math. Phys., vol. 7, World Sci. Publishing, Teaneck, NJ, 1989, pp. 285–339.
  Mathematical Reviews (MathSciNet): MR90m:17022
  Zentralblatt MATH: 0742.17018
  
• [KuR] P. P. Kulish and N. Y. Reshetikhin, Quantum linear problem for the sine-Gordon equation and higher representations, J. Soviet Math. 23 (1983), 2435–2441.
• [K] G. Kuperberg, Spiders for rank $2$ Lie algebras, Comm. Math. Phys. 180 (1996), no. 1, 109–151.
  Mathematical Reviews (MathSciNet): MR97f:17005
  Zentralblatt MATH: 0870.17005
  Digital Object Identifier: doi:10.1007/BF02101184
  Project Euclid: euclid.cmp/1104287237
  
• [L1] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.
  Mathematical Reviews (MathSciNet): MR90m:17023
  Zentralblatt MATH: 0703.17008
  Digital Object Identifier: doi:10.2307/1990961
  JSTOR: links.jstor.org
  
• [L2] G. Lusztig, Canonical bases in tensor products, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 17, 8177–8179.
  Mathematical Reviews (MathSciNet): MR93j:17033
  Zentralblatt MATH: 0760.17011
  Digital Object Identifier: doi:10.1073/pnas.89.17.8177
  JSTOR: links.jstor.org
  
• [L3] G. Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
  Mathematical Reviews (MathSciNet): MR94m:17016
  Zentralblatt MATH: 0788.17010
  
• [MV] G. Masbaum and P. Vogel, $3$-valent graphs and the Kauffman bracket, Pacific J. Math. 164 (1994), no. 2, 361–381.
  Mathematical Reviews (MathSciNet): MR95e:57003
  Zentralblatt MATH: 0838.57007
  Project Euclid: euclid.pjm/1102622100
  
• [M] J. P. Moussouris, Vector coupling coefficients and spin networks, Advances in Twister Theory, Res. Notes Math., vol. 37, Pitman, Boston, 1979, pp. 313–317.
• [P1] R. Penrose, Angular momentum: An approach to combinatorial space-time, Quantum Theory and Beyond ed. T. A. Bastin, Cambridge Univ. Press, Cambridge, 1969.
• [P2] R. Penrose, Applications of negative dimensional tensors, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), Academic Press, London, 1971, pp. 221–244.
  Mathematical Reviews (MathSciNet): MR43:7372
  Zentralblatt MATH: 0216.43502
  
• [Pi] S. Piunikhin, Turaev-Viro and Kauffman-Lins invariants for $3$-manifolds coincide, J. Knot Theory Ramifications 1 (1992), no. 2, 105–135.
  Mathematical Reviews (MathSciNet): MR94g:57010
  Zentralblatt MATH: 0759.57011
  Digital Object Identifier: doi:10.1142/S0218216592000070
  
• [RTW] G. Rumer, E. Teller, and H. Weyl, Eine für die Valenztheorie Geeignete Basis der Binaren Vektorinvarianten, Nachr. Ges. Wiss. Göttingen Math.-Phys. K1. (1932), 499–504.
  Zentralblatt MATH: 0006.14901
  
• [T] V. Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter & Co., Berlin, 1994.
  Mathematical Reviews (MathSciNet): MR95k:57014
  Zentralblatt MATH: 0812.57003
  
• [CFS] J. S. Carter, D. E. Flath, and M. Saito, The classical and quantum 6$j$-symbols, Mathematical Notes, vol. 43, Princeton University Press, Princeton, NJ, 1995.
  Mathematical Reviews (MathSciNet): MR97g:17008
  Zentralblatt MATH: 0851.17001
  
• [CC] L. G. Casian and D. H. Collingwood, The Kazhdan-Lusztig conjecture for generalized Verma modules, Math. Z. 195 (1987), no. 4, 581–600.
  Mathematical Reviews (MathSciNet): MR88i:17008
  Zentralblatt MATH: 0624.22010
  Digital Object Identifier: doi:10.1007/BF01166705
  
• [De] V. V. Deodhar, On some geometric aspects of Bruhat orderings. II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra 111 (1987), no. 2, 483–506.
  Mathematical Reviews (MathSciNet): MR89a:20054
  Zentralblatt MATH: 0656.22007
  Digital Object Identifier: doi:10.1016/0021-8693(87)90232-8
  
• [FKK] I. Frenkel, M. Khovanov, and A. Kirillov, Jr., Kazhdan-Lusztig polynomials and canonical basis, in preparation.
• [FKV] I. Frenkel, A. Varchenko, and A. Kirillov, Jr., Canonical basis and homology of local systems, preprint, 1997.
  Mathematical Reviews (MathSciNet): MR1472345
  Zentralblatt MATH: 0973.17016
  Digital Object Identifier: doi:10.1155/S1073792897000512
  
• [Kh] M. Khovanov, Canonical bases in tensor products $U_q(\mathfraksl_2)$ modules and Jones-Wenzl projectures, preprint, 1996.
• [LS] A. Lascoux and M.-P. Schützenberger, Polynômes de Kazhdan & Lusztig pour les grassmanniennes, Young tableaux and Schur functors in algebra and geometry (Toruń, 1980), Astérisque, vol. 87, Soc. Math. France, Paris, 1981, pp. 249–266.
  Mathematical Reviews (MathSciNet): MR83i:14045
  Zentralblatt MATH: 0504.20007
  
• [V] A. Varchenko, Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Advanced Series in Mathematical Physics, vol. 21, World Scientific Publishing Co. Inc., River Edge, NJ, 1995.
  Mathematical Reviews (MathSciNet): MR99i:32029
  Zentralblatt MATH: 0951.33001