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# Interval Pattern Avoidance for Arbitrary Root Systems

Published:2010-07-26
Printed: Dec 2010
• Alexander Woo,
Department of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, MN, U.S.A.
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## Abstract

We extend the idea of interval pattern avoidance defined by Yong and the author for $S_n$ to arbitrary Weyl groups using the definition of pattern avoidance due to Billey and Braden, and Billey and Postnikov. We show that, as previously shown by Yong and the author for $\operatorname{GL}_n$, interval pattern avoidance is a universal tool for characterizing which Schubert varieties have certain local properties, and where these local properties hold.
 MSC Classifications: 14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 05E15 - Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]