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Subalgebras Which Appear in Quantum Iwasawa Decompositions

Published online by Cambridge University Press:  20 November 2018

Gail Letzter
Gail Letzter*
Affiliation:
Department of Mathematics Whittier College Whittier, CA USA
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Abstract

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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.

Keywords

17B37
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 6 , 01 December 1997 , pp. 1206 - 1223
Copyright
Copyright © Canadian Mathematical Society 1997

References

[DK] 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
[D] Dixmier, J., Algèbres Enveloppantes. Cahiers Scientifiques 37, Gauthier-Villars, Paris, 1974.Google Scholar
[DG] Delius, G. and Gould, M., Quantum Lie algebras, their existence, uniqueness and q-antisymmetry. Preprint, q-alg/9605025.Google Scholar
[GK] 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
[He] Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, New York, 1978.Google Scholar
[Hu] Humphreys, J.E., Introduction to Lie Algebras and Representation Theory. Springer-Verlag, New York, 1972.Google Scholar
[JL1] Joseph, A. and Letzter, G., Local finiteness of the adjoint action for quantized enveloping algebras. J. Algebra 153(1992), 289–318.Google Scholar
[JL2] Joseph, A., Separation of variables for quantized enveloping algebras. Amer. J.Math., 116(1994), 127–177.Google Scholar
[JL3] Joseph, A., Rosso's form and quantized Kac Moody algebras. Math. Z. 222(1996), 543–571.Google Scholar
[K] Kac, V.G., Infinite dimensional Lie algebras. Third edition, Cambridge University Press, New York, 1990.Google Scholar
[L] Lusztig, G., Quantum deformations of certain simple modules over enveloping algebras. Adv. Math. 70(1988), 237–249.Google Scholar
[NS] 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
[R] Rosso, M., Groupes Quantiques, Representations Lineaires et Applications. Thesis Paris 7, (1990).Google Scholar
[S] Sudbery, A., Quantum Lie Algebras of Type An. Preprint, q-alg/9510004.Google Scholar