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

TL;DR

This paper classifies certain right coideal subalgebras of the Borel part of a quantized enveloping algebra, linking them to characters of specific subalgebras and building on recent work on prime ideals.

Contribution

It provides a complete classification of right coideal subalgebras intersecting with the coradical as a Hopf algebra, using character theory and recent prime ideal results.

Findings

Explicit classification of right coideal subalgebras

Determination of all characters of $U^+[w]$

Connection to prime ideals invariant under torus action

Abstract

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