Classification of coideal subalgebras for quantum groups

Stefan Kolb (U Amsterdam)

Wednesday 3rd March, 2010 16:00-17:00 204


In the theory of quantum groups, Lie subalgebras of semisimple Lie algebras should be realised as coideal subalgebras of quantised  enveloping algebras. While many classes of such coideal subalgebras of are known, there is so far no general classification. In this talk, a classification of coideal subalgebras of the positive Borel part of a quantised enveloping algebra is presented. The result is expressed in terms of characters of quantisations of nilpotent Lie subalgebras, which  were introduced by de Concini, Kac, and Procesi for any element in the Weyl group. The study of such characters naturally leads to fun Weyl group combinatorics. The talk is based on joint work with I. Heckenberger. 

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