We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional character χ, we define χ-matroids by a maximality property. For trivial characters, by exploring the combinatorics of incidence stratifications, we provide a set of generators for the Chow vector spaces of the corresponding immanant varieties.
Immanant varieties / Bolognini, Davide; Sentinelli, Paolo. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - ELETTRONICO. - 682:(2024), pp. 164-190. [10.1016/j.laa.2023.11.010]
Immanant varieties
Bolognini Davide;
2024-01-01
Abstract
We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional character χ, we define χ-matroids by a maximality property. For trivial characters, by exploring the combinatorics of incidence stratifications, we provide a set of generators for the Chow vector spaces of the corresponding immanant varieties.| File | Dimensione | Formato | |
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