Schubert varieties and free braidedness

Details Schubert varieties and free braidedness Schubert varieties and free braidedness

2004-03-31

arxiv.org/abs/math/0403551v1

Mathematics

Combinatorics

15 pages, AMSTeX

Scientific paper

We give a simple necessary and sufficient condition for a Schubert variety $X_w$ 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 (math.CO/0301104). 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.

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