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Homogeneous right coideal subalgebras of quantized enveloping algebras

Lookup NU author(s): Dr Stefan Kolb

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Abstract

For a quantized enveloping algebra of a complex semisimple Lie algebra with deformation parameter not a root of unity, we classify all homogeneous right coideal subalgebras. Any such right coideal subalgebra is determined uniquely by a triple consisting of two elements of the Weyl group and a subset of the set of simple roots satisfying some natural conditions. The essential ingredients of the proof are the Lusztig automorphisms and the classification of homogeneous right coideal subalgebras of the Borel Hopf subalgebras of quantized enveloping algebras obtained previously by H.-J. Schneider and the first-named author.

Publication metadata

Author(s): Heckenberger I, Kolb S

Publication type: Article

Publication status: Published

Journal: Bulletin of the London Mathematical Society

Year: 2012

Volume: 44

Issue: 4

Pages: 837-848

Print publication date: 05/04/2012

ISSN (print): 0024-6093

ISSN (electronic): 1469-2120

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1112/blms/bds027

DOI: 10.1112/blms/bds027

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