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- W2000325090 abstract "Ici on étudie la R-matrice des algèbres quantiques de type affine non tordu : grâce aux résultats contenus dans [8], [25], [26] il s'agit de trouver une base de Uq+ et une Uq− duales par rapport à la forme de Killing. Après avoir rappelé les notations (1 et 2), les résultats généraux (2, 3) et ceux connus pour le cas fini - et conséquemment pour les racines réelles - (4), le premier pas est d'étudier l'action du coproduit sur les vecteurs relatifs aux racines imaginaires (5 et 7), en utilisant les propriétés de commutation analysées dans 6. Ensuite on décrit quelques propriétés de dualité des bases de PBW (8) et on calcule la forme de Killing sur les vecteurs relatifs aux racines imaginaires (9), pour conclure enfin avec l'étude complète des propriétés de dualité (10). On résume donc les résultats dans la formule exponentielle pour la R-matrice (11). This paper deals with the study of the R-matrix for non-twisted affine quantum algebras: thanks to the results of [8], [25], [26] this problem reduces to looking for dual bases of Uq+ and Uq− (dual with respect to the Killing form). After recalling the notations (1 and 2), the general results (2 and 3) and the well known facts about the finite case and the real root vectors (4), the first step consists in studying the action of the coproduct on the imaginary root vectors (5 and 7) by applying the commutation rules found in 6. The second step is describing some duality properties of the PBW-bases (8), computing the Killing form on the imaginary root vectors (9) and finally giving complete details on the duality properties (10). These results are gathered together in 11, where an explicit exponential formula for the R-matrix is given." @default.
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- W2000325090 date "1998-07-01" @default.
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- W2000325090 title "La R-matrice pour les algèbres quantiques de type affine non tordu1" @default.
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- W2000325090 doi "https://doi.org/10.1016/s0012-9593(98)80104-3" @default.
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