Séminaire Lotharingien de Combinatoire, 91B.71 (2024), 9 pp.
Leo Jiang
Real Matroid Schubert Varieties, Zonotopes, and Virtual Weyl Groups
Abstract.
We show that the matroid Schubert variety of a real hyperplane arrangement is homeomorphic to the zonotope of the arrangement with parallel faces identified.
Using this explicit model, we compute the homology and fundamental group of the matroid Schubert variety in terms of combinatorial data of the underlying oriented matroid.
When the hyperplane arrangement is a Coxeter arrangement, we show that the equivariant fundamental group is a virtual analogue of the associated Weyl group.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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