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# Subalgebras which appear in quantum Iwasawa decompositions

Published:1997-12-01
Printed: Dec 1997
• Gail Letzter
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## Abstract

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.
 MSC Classifications: 17B37 - Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]