(1) Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO 80309-0395, USA;(2) Department of Mathematics, Long Island University, 720 Northern Boulevard, Brookville, NY 11548-1319, USA
Abstract:
We give a simple necessary and sufficient condition for a Schubert variety Xw to be smooth when w is a freely braided element of a simply laced Weyl group; such elements were introduced by the authors in a previous work. This generalizes in one direction a result of Fan concerning varieties indexed by short-braid avoiding elements. We also derive generating functions for the freely braided elements that index smooth Schubert varieties. All results are stated and proved only for the simply laced case.
