Right coideal subalgebras of the Borel part of a quantized enveloping algebra

Details Right coideal subalgebras of the Borel part of a quantized enveloping algebra Right coideal subalgebras of the Borel part of a quantized enveloping algebra

2009-10-19

arxiv.org/abs/0910.3505v1

Mathematics

Quantum Algebra

21 pages

Scientific paper

For the Borel part of a quantized enveloping algebra we classify all right coideal subalgebras for which the intersection with the coradical is a Hopf algebra. The result is expressed in terms of characters of the subalgebras $U^+[w]$ of the quantized enveloping algebra, introduced by de Concini, Kac, and Procesi for any Weyl group element $w$. We explicitly determine all characters of $U^+[w]$ building on recent work by Yakimov on prime ideals of $U^+[w]$ which are invariant under a torus action. Key words: Quantum groups, coideal subalgebras

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