Weyl group action and semicanonical bases
arXiv:1104.0907 · doi:10.1016/j.aim.2011.07.021
Abstract
Let U be the enveloping algebra of a symmetric Kac-Moody algebra. The Weyl group acts on U, up to a sign. In addition, the positive subalgebra U^+ contains a so-called semicanonical basis, with remarkable properties. The aim of this paper is to show that these two structures are as compatible as possible.