Braid group actions on coideal subalgebras of quantized enveloping algebras

Abstract

We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair ( sl 2 n ( C ) , sp 2 n ( C ) ) . This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric simple complex Lie algebras. The given actions are inspired by Lusztigʼs braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.