Canonical bases arising from quantized enveloping algebras
Author:
G. Lusztig
Journal:
J. Amer. Math. Soc. 3 (1990), 447-498
MSC:
Primary 17B35; Secondary 16A64
DOI:
https://doi.org/10.1090/S0894-0347-1990-1035415-6
MathSciNet review:
1035415
Full-text PDF Free Access
References | Similar Articles | Additional Information
- [BBD] A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- [BZ] A. D. Berenstein and A. V. Zelevinsky, Tensor product multiplicities and convex polytopes in partition space, J. Geom. Phys. 5 (1988), no. 3, 453–472. MR 1048510, https://doi.org/10.1016/0393-0440(88)90033-2
- [BGP] I. N. Bernšteĭn, I. M. Gel′fand, and V. A. Ponomarev, Coxeter functors, and Gabriel’s theorem, Uspehi Mat. Nauk 28 (1973), no. 2(170), 19–33 (Russian). MR 0393065
- [B] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- [DK] Corrado De Concini and David Kazhdan, Special bases for 𝑆_{𝑁} and 𝐺𝐿(𝑛), Israel J. Math. 40 (1981), no. 3-4, 275–290 (1982). MR 654583, https://doi.org/10.1007/BF02761368
- [DL]
M. Dyer and G. Lusztig, Appendix to
, Geom. Dedicata (to appear).
- [G] Peter Gabriel, Unzerlegbare Darstellungen. I, Manuscripta Math. 6 (1972), 71–103; correction, ibid. 6 (1972), 309 (German, with English summary). MR 332887, https://doi.org/10.1007/BF01298413
- [KL1] David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, https://doi.org/10.1007/BF01390031
- [KL2] David Kazhdan and George Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203. MR 573434
- [L1] George Lusztig, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra, J. Amer. Math. Soc. 3 (1990), no. 1, 257–296. MR 1013053, https://doi.org/10.1090/S0894-0347-1990-1013053-9
- [L2] George Lusztig, Quantum groups at roots of 1, Geom. Dedicata 35 (1990), no. 1-3, 89–113. MR 1066560, https://doi.org/10.1007/BF00147341
- [L3] G. Lusztig, Left cells in Weyl groups, Lie group representations, I (College Park, Md., 1982/1983) Lecture Notes in Math., vol. 1024, Springer, Berlin, 1983, pp. 99–111. MR 727851, https://doi.org/10.1007/BFb0071433
- [L4] G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), no. 2, 169–178. MR 641425, https://doi.org/10.1016/0001-8708(81)90038-4
- [R] Claus Michael Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), no. 3, 583–591. MR 1062796, https://doi.org/10.1007/BF01231516
- [Z] A. V. Zelevinskiĭ, Two remarks on graded nilpotent classes, Uspekhi Mat. Nauk 40 (1985), no. 1(241), 199–200 (Russian). MR 783619
Retrieve articles in Journal of the American Mathematical Society with MSC: 17B35, 16A64
Retrieve articles in all journals with MSC: 17B35, 16A64
Additional Information
DOI:
https://doi.org/10.1090/S0894-0347-1990-1035415-6
Article copyright:
© Copyright 1990
American Mathematical Society