Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903821 | Journal of Combinatorial Theory, Series A | 2018 | 18 Pages |
Abstract
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 introduce the notion of a split pattern and 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. Continuing, we 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 635241. This extends a combined result of Lakshmibai-Sandhya, Ryan, and Wolper who prove that Schubert varieties whose permutation avoids the “smooth” patterns 3412 and 4231 are iterated fiber bundles of smooth Grassmannian Schubert varieties.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Timothy Alland, Edward Richmond,