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Interval pattern avoidance for arbitrary root systems
We extend the idea of interval pattern avoidance defined by Yong and the
author for 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 , interval pattern avoidance
is a universal tool for characterizing which Schubert varieties have certain
local properties, and where these local properties hold.Comment: 6 page
When is a Schubert variety Gorenstein?
A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical
sheaf is a line bundle. This property, which measures the ``pathology'' of the
singularities of a variety, is thus stronger than Cohen-Macualayness, but is
also weaker than smoothness. We determine which Schubert varieties are
Gorenstein in terms of a combinatorial characterization using generalized
pattern avoidance conditions. We also give an explicit description as a line
bundle of the canonical sheaf of a Gorenstein Schubert variety.Comment: 15 pages, geometric characterization of Gorensteinness added; final
version to appear in Adv. Mat
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