Smoothness of Schubert varieties via patterns in root subsystems

@inproceedings{Billey2005SmoothnessOS,
  title={Smoothness of Schubert varieties via patterns in root subsystems},
  author={Sara Billey and Alexander Postnikov},
  year={2005}
}
The aim of this article is to present a smoothness criterion for Schubert varieties in gene flag manifoldsG/B in terms of patterns in root systems. We generalize Lakshmibai–Sandhya’s known result that says that a Schubert variety in SL(n)/B is smooth if and only if the correspondin permutation avoids the patterns 3412 and 4231. Our criterion is formulated uniformly in gene theoretic terms. We define a notion of pattern in Weyl group elements and show that a Schu riety is smooth (or rationally… CONTINUE READING
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