Séminaire Lotharingien de Combinatoire, 78B.7 (2017), 12 pp.
Timothy Alland and Edward Richmond
Pattern Avoidance and Fiber Bundle Structures on Schubert Varieties
We give a permutation pattern avoidance criteria for determining when
the projection map from the flag variety to a Grassmannian induces a
fiber bundle structure on a Schubert variety. In particular, we show
that a Schubert variety has such a fiber bundle structure if and only
if the corresponding permutation avoids the split patterns 3|12 and
23|1. We also show that a Schubert variety is an iterated fiber
bundle of Grassmannian Schubert varieties if and only if the
corresponding permutation avoids (non-split) patterns 3412, 52341, and
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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