  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_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev
and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras.
The given actions are inspired by Lusztig's 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.
