Quantized GIM lie algebras and their Lusztig symmetries

We study quantized universal enveloping algebras of Slodowy's GIM Lie algebras. It is shown that they have Lusztig symmetries associated to the corresponding toroidal Weyl groups, and these symmetries satisfy the braid relations given by the toroidal root systems. (c) 2005 Elsevier Inc. All rights reserved.