Parametrizations of canonical bases and irreducible components of nilpotent varieties
arXiv:1110.2937
Abstract
It is known that the set of irreducible components of nilpotent varieties provides a geometric realization of the crystal basis for quantum groups. For each reduced expression of a Weyl group element, Geiß, Leclerc and Schröer has recently given a parametrization of irreducible components of nilpotent varieties in studying cluster algebras. In this paper we show that their parametrization coincides with Lusztig's parametrization of the canonical basis.
revised version, 11 pages