La $R$-matrice pour les algèbres quantiques de type affine non tordu

Damiani, Ilaria

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 4, pp. 493-523.

[1] J. Beck, Braid group action and quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 555-568). | MR | Zbl

[2] J. Beck, Convex bases of PBW type for quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 193-199). | MR | Zbl

[3] N. Bourbaki, Groupes et algèbres de Lie 4, 5, 6, Hermann, Paris, 1968.

[4] I. Damiani, The Highest Coefficient of detHη and the Center of the Specialization at Odd Roots of Unity for Untwisted Affine Quantum Algebras, (J. Algebra, vol. 186, 1996, p. 736-780). | MR | Zbl

[5] I. Damiani et C. De Concini, Quantum groups and Poisson groups in (Baldoni-Picardello, Representations of Lie groups and quantum groups, Longman Scientific and Technical, 1994, p. 1-45). | MR | Zbl

[6] C. De Concini, V. G. Kac, Representations of quantum groups at roots of 1, (Progr. in Math., vol. 92, 1990, p. 471-506, Birkhäuser). | MR | Zbl

[7] V. G. Drinfeld, A new realization of Yangians and quantized affine algebras, (Soviet Math. Dokl., vol. 36, 1988, n° 2, p. 212-216). | MR | Zbl

[8] V. G. Drinfeld, Hopf algebras and quantum Yang-Baxter equation, (Soviet Math. Dokl., vol. 32, 1985, p. 254-258). | MR | Zbl

[9] V. G. Drinfeld, Quantum groups, (Proc. ICM, Berkeley, 1986, p. 798-820). | MR | Zbl

[10] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, (Springer-Verlag, USA 1972). | MR | Zbl

[11] M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, (Lett. Math. Phys., vol. 10, 1985, p. 63-69). | MR | Zbl

[12] V. G. Kac, Infinite Dimensional Lie Algebras, (Birkhäuser Boston, Inc., USA, 1983). | MR | Zbl

[13] V. G. Kac et D. A. Kazhdan, Structure of representations with highest weight of infinite-dimensional Lie algebras, (Adv. Math., vol. 34, 1979, p. 97-108). | MR | Zbl

[14] S. M. Khoroshkin et V. N. Tolstoy, Universal R-matrix for quantized(super) algebras, (Commun. Math. Phys., vol. 141, 1991, p. 599-617). | MR | Zbl

[15] S. M. Khoroshkin et V. N. Tolstoy, The universal R-matrix for quantum nontwisted affine Lie algebras, (Funkz. Analiz i ego pril., vol. 26:1, 1992, p. 85-88). | Zbl

[16] A. N. Kirillov et N. Reshetikhin, q-Weyl Group and a Multiplicative Formula for Universal R-Matrices, (Commun. Math. Phys., vol. 134, 1990, p. 421-431). | MR | Zbl

[17] S. Z. Levendorskii et Ya. S. Soibelman, Quantum Weyl group and multiplicative formula for the R-matrix of a simple Lie algebra, (Funct. Analysis and its Appl., 2 vol. 25, 1991, p. 143-145). | MR | Zbl

[18] S. Z. Levendorskii et Ya. S. Soibelman, Some applications of quantum Weyl group I, (J. Geom. Phys., vol. 7, 1990, p. 241-254). | MR | Zbl

[19] S. Z. Levendorskii, Ya. S. Soibelman et V. Stukopin, The Quantum Weyl Group and the Universal Quantum R-Matrix for Affine Lie Algebra A(1)1, (Lett. Math. Phys., vol. 27, 1993, p. 253-264). | MR | Zbl

[20] G. Lusztig, Finite-dimensional Hopf algebras arising from quantum groups, (J. Amer. Math. Soc., vol. 3, 1990, p. 257-296). | MR | Zbl

[21] G. Lusztig, Introduction to quantum groups, (Birkhäuser Boston, USA, 1993). | MR | Zbl

[22] G. Lusztig, Quantum groups at roots of 1, (Geom. Ded., vol. 35, 1990, p. 89-113). | MR | Zbl

[23] H. Matsumoto, Générateurs et relations des groupes de Weyl généralisés, (C. R. Acad. Sci. Paris, tome 258, Série II, 1964, p. 3419-3422). | MR | Zbl

[24] M. Rosso, An Analogue of P.B.W. Theorem and the Universal R-Matrix for Uhsl(N + 1), (Commun. Math. Phys., vol. 124, 1989, p. 307). | MR | Zbl

[25] M. Rosso, Certaines formes bilinéaires sur les groupes quantiques et une conjecture de Schechtman et Varchenko, (C. R. Acad. Sci. Paris, tome 314, Série I, 1992, p. 5-8). | MR | Zbl

[26] T. Tanisaki, Killing forms, Harish-Chandra isomorphisms and universal R-matrices for Quantum Algebras, in (Infinite Analysis Part B, Adv. Series in Math. Phys., vol. 16, 1992, p. 941-962). | MR | Zbl