Right Coideal Subalgebras of the Borel Part of a Quantized Enveloping Algebra

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.