|
On an inner product in modular tensor categories
Author(s):
Alexander
A.
Kirillov Jr.
Journal:
J. Amer. Math. Soc.
9
(1996),
1135-1169.
MSC (1991):
Primary 81R50, 05E35, 18D10;
Secondary 57M99
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
References |
Similar articles |
Additional information
References:
- [A]
- Andersen, H. H., On tensor products of quantized tilting modules, Com. Math. Phys. 149 (1992), 149--159. MR 94b:17015
- [AI]
- Askey, R. and Ismail, M.E.H., A generalization of ultraspherical polynomials, Studies in Pure Mathematics (P. Erdös, ed.), Birkhäuser, 1983, pp. 55--78. MR 87a:33015
- [AP]
- Andersen, H. H. and Paradowski, J., Fusion categories arising from semisimple Lie algebras, Com. Math. Phys 169 (1995), 563--588. CMP 95:11
- [Ch]
- Cherednik, I., Macdonald's evaluation conjectures and difference Fourier transform, preprint, May 1995, q-alg/9412016. CMP 96:02
- [Dr1]
- Drinfeld, V.G., Quantum groups, Proc. Int. Congr. Math., Berkeley, 1986, pp. 798--820. MR 89f:17017
- [Dr2]
- ------, On almost cocommutative Hopf algebras, Leningrad Math.J. 1 (2) (1990), 321--342. MR 91b:16046
- [EK1]
- Etingof, P.I. and Kirillov, A.A., Jr, A unified representation-theoretic approach to special functions, Functional Anal. and its Applic. 28 (1) (1994), 91--94. MR 95h:33010
- [EK2]
- ------, Macdonald's polynomials and representations of quantum groups, Math. Res. Let. 1 (1994), 279--296. CMP 95:04
- [EK3]
- ------, Representation-theoretic proof of inner product and symmetry identities for Macdonald's polynomials, hep-th/9410169, to appear in Comp. Math. (1995).
- [F]
- Finkelberg, M., Fusion categories, Ph.D thesis, Harvard Univ. (1993), (to appear in GAFA).
- [GK]
- Gelfand, S. and Kazhdan, D., Examples of tensor categories, Invent. Math. 109 (1992), 595--617. MR 93m:20057
- [Kac]
- Kac, V.G., Infinite-dimensional Lie algebras, 3rd ed., Cambridge Univ. Press, 1990. MR 92k:17038
- [Kas]
- Kassel, C., Quantum groups, Springer, New York, 1995. CMP 95:09
- [KL1]
- Kazhdan, D. and Lusztig, G., Tensor structures arising from affine Lie algebras. I, J. of AMS 6 (1993), 905--947. MR 93m:17014
- [KL2]
- ------, Tensor structures arising from affine Lie algebras. II, J. of AMS 6 (1993), 949--1011. MR 93m:17014
- [KL3]
- ------, Tensor structures arising from affine Lie algebras. III, J. of AMS 7 (1994), 335--381. MR 94g:17048
- [KL4]
- ------, Tensor structures arising from affine Lie algebras. IV, J. of AMS 7 (1994), 383--453. MR 94g:17049
- [Ke]
- Kerler, T., Mapping class group actions on quantum doubles, Comm. Math. Phys. 168 (1995), 353--388. CMP 95:10
- [KR]
- Kirillov, A.N. and Reshetikhin, N.Yu., q-Weyl group and a multiplicative formula for universal R-matrices, Comm. Math. Phys. 134 (1990), 421--431. MR 92c:17023
- [L1]
- Lusztig, G., Modular representations and quantum groups, Contemp. Math., vol. 82, AMS, Providence, 1989, pp. 52--77. MR 90a:16008
- [L2]
- ------, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebras, J. of AMS 3 (1990), 257--296. MR 91e:17009
- [L3]
- ------, Quantum groups at roots of 1, Geom. Dedicat. 35 (1990), 89--113. MR 91j:17018
- [L4]
- ------, On quantum groups, J. of Algebra 131 (1990), 466--475. MR 91j:17019
- [L5]
- ------, Introduction to quantum groups, Birkhäuser, Boston, 1993. MR 94m:17016
- [L6]
- ------, Monodromic systems on affine flag manifolds, Proc. R. Soc. Lond. A 445 (1994), 231--246. MR 95m:20049
- [L7]
- ------, Canonical bases arising from quantized enveloping algebras. II, Progr. Theor. Phys. Suppl. 102 (1990), 175--201. MR 93g:17019
- [LS]
- Levendorskii, S.Z. and Soibelman, Ya. S., Some applications of quantum Weyl groups, Jour. Geom. Phys. 7 (2) (1990), 241--254. MR 92g:17016
- [Lyu]
- Lyubashenko, V., Modular transformations for tensor categories, J. Pure Appl. Algebra 98 (1995), 279--327. CMP 95:10
- [M1]
- Macdonald, I.G., A new class of symmetric functions, Publ. I.R.M.A. Strasbourg, 372/S-20, Actes 20 Séminaire Lotharingien (1988), 131-171.
- [M2]
- ------, Orthogonal polynomials associated with root systems, preprint (1988).
- [Mac]
- MacLane, S., Categories for working mathematician, Graduate Texts in Mathematics, vol. 5, Springer--Verlag, New York, 1971. MR 50:7275
- [MS1]
- Moore, G., Seiberg, N., Classical and quantum conformal field theory, Com. Math. Phys. 123 (1989), 177--254. MR 90e:81216
- [MS2]
- ------, Lectures on RCFT, Superstrings '89 (Proc. of the 1989 Trieste Spring School) (M. Green et al, eds.), World Sci., River Edge, NJ, 1990, pp. 1--129. MR 93m:81133a
- [MS3]
- ------, Polynomial equations for rational conformal field theories, Phys. Let. B212 (1988), 451--460. MR 89m:81155
- [MS4]
- ------, Naturality in conformal field theory, Nucl. Phys. B313 (1989), 16--40. MR 90f:81119
- [RT1]
- Reshetikhin, N. and Turaev, V., Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), 1--26. MR 91c:57016
- [RT2]
- ------, Invariants of 3-manifolds via link polynomials and quantum groups, Inv. Math. 103 (1991), 547-597. MR 92b:57024
- [Tu]
- Turaev, V., Quantum invariants of knots and 3-manifolds, W. de Gruyter, Berlin, 1994. MR 95k:57014
- [Vaf]
- Vafa, C., Towards classification of conformal theories, Phys. Lett. B 206 (1988), 421--426. MR 89k:81178
- [We]
- Wenzl, H., Quantum groups and subfactors of type B, C, and D, Comm. Math. Phys. 133 (1990), 383--433. MR 92k:17032
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with MSC
(1991):
81R50, 05E35, 18D10,
57M99
Retrieve articles in all Journals with MSC
(1991):
81R50, 05E35, 18D10,
57M99
Additional Information:
Alexander
A.
Kirillov
Jr.
Affiliation:
Department of Mathematics, Massachusetts Institite of Technology, Cambridge, Massachusetts 02139
Email:
kirillov@math.mit.edu
DOI:
10.1090/S0894-0347-96-00210-X
PII:
S 0894-0347(96)00210-X
Keywords:
Modular tensor categories,
quantum groups at roots of 1,
Macdonald polynomials
Received by editor(s):
October 12, 1995
Received by editor(s) in revised form:
November 20, 1995
Dedicated:
Dedicated to my father on his 60th birthday
Copyright of article:
Copyright
1996,
American Mathematical Society
|