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Cluster-Permutohedra and Submanifolds of Flag Varieties with Torus Actionsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Ayzenberg Anton, Buchstaber Victor
- Журнал: International Mathematics Research Notices
- Год издания: 2023
- Издательство: Oxford University Press
- Местоположение издательства: United Kingdom
- Первая страница: 1
- Последняя страница: 28
- DOI: 10.1093/imrn/rnad076
- Аннотация: In this paper, we describe a relation between the notion of graphicahedron, introduced by Araujo-Pardo, Del Río-Francos, López-Dudet, Oliveros, and Schulte in 2010 and toric topology of manifolds of sparse isospectral Hermitian matrices. More precisely, we recall the notion of a cluster-permutohedron, a certain finite poset defined for a simple graph G. This poset is build as a combination of cosets of the symmetric group, and the geometric lattice of the graphical matroid of G. This poset is similar to the graphicahedron of G, in particular, 1-skeleta of both posets are isomorphic to Cayley graphs of the symmetric group. We describe the relation between cluster-permutohedron and graphicahedron using Galois connection and the notion of a core of a finite topology. We further prove that the face poset of the natural torus action on the manifold of isospectral G-shaped Hermitian matrices is isomorphic to the cluster-permutohedron. Using recent results in toric topology, we show that homotopy properties of graphicahedra may serve an obstruction to equivariant formality of isospectral matrix manifolds. We introduce a generalization of a cluster-permutohedron and describe the combinatorial structure of a large family of manifolds with torus actions, including Grassmann manifolds and partial flag manifolds.
- Добавил в систему: Бухштабер Виктор Матвеевич