Canonical bases arising from quantized enveloping algebras
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References
- 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
- 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, DOI 10.1016/0393-0440(88)90033-2
- 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
- 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 [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Corrado De Concini and David Kazhdan, Special bases for $S_{N}$ and $\textrm {GL}(n)$, Israel J. Math. 40 (1981), no. 3-4, 275–290 (1982). MR 654583, DOI 10.1007/BF02761368 M. Dyer and G. Lusztig, Appendix to $[{\text {L2}}]$, Geom. Dedicata (to appear).
- Peter Gabriel, Unzerlegbare Darstellungen. I, Manuscripta Math. 6 (1972), 71–103; correction, ibid. 6 (1972), 309 (German, with English summary). MR 332887, DOI 10.1007/BF01298413
- David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
- 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
- George Lusztig, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra, J. Amer. Math. Soc. 3 (1990), no. 1, 257–296. MR 1013053, DOI 10.1090/S0894-0347-1990-1013053-9
- George Lusztig, Quantum groups at roots of $1$, Geom. Dedicata 35 (1990), no. 1-3, 89–113. MR 1066560, DOI 10.1007/BF00147341
- 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, DOI 10.1007/BFb0071433
- G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), no. 2, 169–178. MR 641425, DOI 10.1016/0001-8708(81)90038-4
- Claus Michael Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), no. 3, 583–591. MR 1062796, DOI 10.1007/BF01231516
- A. V. Zelevinskiĭ, Two remarks on graded nilpotent classes, Uspekhi Mat. Nauk 40 (1985), no. 1(241), 199–200 (Russian). MR 783619
Additional Information
- © Copyright 1990 American Mathematical Society
- 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