Geodesic
Subalgebras Which Appear in Quantum Iwasawa Decompositions
Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1206-1223

Voir la notice de l'article provenant de la source Cambridge University Press

Let g be a semisimple Lie algebra. Quantum analogs of the enveloping algebra of the fixed Lie subalgebra are introduced for involutions corresponding to the negative of a diagram automorphism. These subalgebras of the quantized enveloping algebra specialize to their classical counterparts. They are used to form an Iwasawa type decompostition and begin a study of quantum Harish-Chandra modules.
DOI : 10.4153/CJM-1997-059-4
Mots-clés : 17B37 
Letzter, Gail. Subalgebras Which Appear in Quantum Iwasawa Decompositions. Canadian journal of mathematics, Tome 49 (1997) no. 6, pp. 1206-1223. doi: 10.4153/CJM-1997-059-4
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DeConcini, C., and Kac, V.G., Representations of quantum groups at roots of 1. In: Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Prog. Math. 92(1990), 471–506. Google Scholar

Dixmier, J., Algèbres Enveloppantes. Cahiers Scientifiques 37, Gauthier-Villars, Paris, 1974. Google Scholar

Delius, G. and Gould, M., Quantum Lie algebras, their existence, uniqueness and q-antisymmetry. Preprint, q-alg/9605025. Google Scholar

Gavrilik, A.M. and Klimyk, A.U., q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations. Lett. Math. Phys. 21(1991), 215–220. Google Scholar

Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, New York, 1978. Google Scholar

Humphreys, J.E., Introduction to Lie Algebras and Representation Theory. Springer-Verlag, New York, 1972. Google Scholar

Joseph, A. and Letzter, G., Local finiteness of the adjoint action for quantized enveloping algebras. J. Algebra 153(1992), 289–318. Google Scholar

Joseph, A., Separation of variables for quantized enveloping algebras. Amer. J.Math., 116(1994), 127–177. Google Scholar

Joseph, A., Rosso's form and quantized Kac Moody algebras. Math. Z. 222(1996), 543–571. Google Scholar

Kac, V.G., Infinite dimensional Lie algebras. Third edition, Cambridge University Press, New York, 1990. Google Scholar

Lusztig, G., Quantum deformations of certain simple modules over enveloping algebras. Adv. Math. 70(1988), 237–249. Google Scholar

Noumi, M. and Sugitani, T., Quantum symmetric spaces and related q-orthogonal polynomials. Group TheoreticalMethods in Physics (ICGTMP) (Toyonaka, Japan, 1994.,World Sci. Publishing, River Edge, NJ, 1995. 28–40. Google Scholar

Rosso, M., Groupes Quantiques, Representations Lineaires et Applications. Thesis Paris 7, (1990). Google Scholar

Sudbery, A., Quantum Lie Algebras of Type An. Preprint, q-alg/9510004. Google Scholar

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