Quantum groups and subfactors of type B, C, and D

Springer Science and Business Media LLC - Tập 133 Số 2 - Trang 383-432 - 1990
Hans Wenzl1
1University of California, San Diego, La Jolla, USA

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Tài liệu tham khảo

[AGS] Alvarez-Gaume, L., Gomez, C., Sierra, G.: Duality and quantum groups, preprint, CERN

[B] Birman, J.: Braids, link and mapping class groups. Ann. Math. Studies vol. 82, Princeton, NJ: Princeton University Press 1974

[BW] Birman, J., Wenzl, H.: Braids, link polynomials and a new algebra. Trans. AMS313, 249–273 (1989)

[Bk] Bourbaki, N.: Groupes et Algèbres de Lie, IV–VI

[Br] Brauer, R.: On algebras which are connected with the semisimple continuous groups. Ann. Math.63, 854–872 (1937)

[DJ1] Dipper, R., James, G.: Repr. of Hecke algebras of the general linear group. Proc. LMS52, 20–52 (1986)

[DJ2] Dipper, R., James, G.: Blocks and idempotents of the Hecke algebra of the general linear group. Proc. LMS54, 57–82 (1987)

[D] Drinfeld, V.: Quantum groups, Proceedings for the ICM Berkeley, 1986, pp. 798–820

[EK] El Samra, N., King, R.: Dimensions of irreducible representations of the classical Lie groups. J. Phys. A: Math. Gen.12, 2317–2328 (1979)

[FRS] Fredenhagen, K., Rehren, K.H., Schroer, B.: Superselection sector with braid statistic and exchange algebra, General Theory. Commun. Math. Phys.125, 201–226 (1989)

[FYHLMO] Freyd, P., Yetter, D., Hoste, J., Lickorish, W.B.R., Millett, K., Ocneanu, A.: A new polynomial invariant of knots and links. Bull. AMS12, No. 2, 239–246 (1985)

[FFK] Felder, G., Fröhlich, J., Keller, G.: Braid matrices and structure constants for minimal conformal models, Commun. Math. Phys.124, 647–664 (1990)

[GM] Garsia, A., McLarnan, T.: Relations between Young's natural and the Kazhdan-Lusztig representations ofS n. Adv. Math.69, 32–92 (1988)

[GW] Goodman, F., Wenzl, H.: Littlewood Richardson coefficients for Hecke algebras at roots of unity. Adv. Math (1990)

[G] Gyoja, A.: Aq-analogue of Young symmetrizer. Osaka J. Math.23, 841–852 (1986)

[HS] Haagerup, U., Schou, J.: Examples of subfactors, preprint Odense University

[H] Hoefsmit, P.N.: Representations of Hecke algebras of finite groups with BN pairs of classical type, thesis, University of British Columbia (1974)

[Ji-1] Jimbo, M.: QuantumR-matrix for the generalized Toda system. Commun. Math. Phys.102, 537–547 (1986)

[Ji-2] Jimbo, M.: Aq analogue ofU(gl(N+1)), Hecke algebras and the Yang-Baxter equation. Lett. Math. Phys.10, 63–69 (1985)

[Ji-3] Jimbo, M.: Introduction to the Yang-Baxter equation. Braid Group, Knot Theory and Statistical Mechanics, pp. 111–134. World Scientific (1989)

[JMO] Jimbo, M., Miwa, T., Okado, M.: Solvable lattice models related to the vector representations of classical simple Lie algebras. Commum. Math. Phys.116, 507–525 (1988)

[Jo-1] Jones, V.F.R.: Index for subfactors. Invent Math.72, 1–25 (1983)

[Jo-2] Jones, V.F.R.: Hecke algebra representations of braid groups and link polynomials. Ann. Math.126, 335–388 (1987)

[Jo-3] Jones, V.F.R.: On knot invariants related to some statistical mechanics models. Pacific J. Math. (1989)

[Kc] Kac, V.: Infinite dimensional Lie algebras, 3rd edition

[K] Kauffman, L.H.: An invariant of regular isotopy. Trans. AMS318, 417–471 (1990)

[KL] Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent Math.53, 165–184 (1979)

[Ko] Kohno, T.: Ann. Inst. Four.

[L] Lusztig, G.: Quantum deformations of certain simple modules over enveloping algebras. Adv. Math.70, 237–249 (1988)

[MW] Morton, H., Wassermann, A.: A basis for the Birman-Wenzl algebra, preprint

[M-1] Murakami, J.: The Kauffman polynomial of links and representation theory. Osaka J. Math.24, 745–758 (1987)

[M-2] Murakami, J.: The parallel version of link invariants, preprint

[O] Ocneanu, A.: Quantized groups, string algebras and Galois theory for algebras. Lond. Math. Soc. Lect. Notes vol.136, Evans/Takesaki (ed.) pp. 119–172

[Pa] Pasquier, V.: Etiology of IRF models. Commun. Math. Phys.118, 355–364 (1986)

[Pi] Pimsner, M.: A class of Markov traces, preprint, University of Heidelberg

[PP] Pimsner, M., Popa, S.: Entropy and index for subfactors. Ann. Sci. Ec. Norm. Sup.19, 57–106 (1986)

[Po] Popa, S.: On the classification of subfactors. Invent. Math.101, 19–43 (1990)

[RW] Ram, A., Wenzl, H.: Matrix units for centralizer algebras. J. of Algebras (to appear)

[Re] Reshetikhin, N.Yu.: Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, LOMI preprint

[Ro] Rosso, M.: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra. Commun. Math. Phys.117, 581–593 (1988)

[T] Turaev, V.G.: The Yang-Baxter equation and invariants of links, Invent. Math.92, 527–553 (1988)

[Wa] Wassermann, A.: Coactions and Yang-Baxter equations for ergodic actions and subfactors, Lond. Math. Soc. Lect. Notes136, Evans/Takesaki (ed.), pp. 203–236

[W-1] Wenzl, H.: Hecke algebras of typeA n and subfactors, Invent Math.92, 349–383 (1988)

[W-2] Wenzl, H.: On the structure of Brauer's centralizer algebras, Ann. Math.128, 173–193 (1988)

[W-3] Wenzl, H.: Representations of braid groups and the quantum Yang-Baxter equation. Pacific J. Math. (1990)

[W-4] Wenzl, H.: Unitarizations of solutions of the quantum Yang-Baxter equation and subfactors. Proc. Congress IAMP, Swansea, 1988 (to appear)

[W-5] Wenzl, H.: Quantum groups and subfactors of Lie type B, C and D, preprint

[Wy] Weyl, H.: The classical groups. Princeton, NJ: Princeton University Press

[Y] Yamane, H.: Irreducible projective modules of the Hecke algebras of a finite Coxeter group, preprint, Osaka University