Quantum subgroups of simple twisted quantum groups at roots of one

Abstract

Let $G$ be a connected, simply connected simple complex algebraic group and let $\epsilon$ be a primitive $\ell$th root of unity with $\ell$ odd and coprime with $3$ if $G$ is of type $G_2$. We determine all Hopf algebra quotients of the twisted multiparameter quantum function algebra ${\mathcal{O}}_{\epsilon }^{\phi }(G)$ introduced by Costantini and Varagnolo. This extends the results of Andruskiewitsch and the first author, where the untwisted case is treated.

30 pages, Several diagrams. This version: minor typos corrected. To appear in Transactions of the AMS