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arXiv · 1609.04507

Matroidal Schur Algebras

Tom Braden·Carl Mautner
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Abstract

Fix a principal ideal domain $k$. In this article we associate to a (weighted) matroid $M$ a quasi-hereditary algebra $R(M)$ defined over $k$ such that matroid duality corresponds to Ringel duality of quasi-hereditary algebras. The representation theory of these algebras is related to work of Schechtman-Varchenko and Brylawski-Varchenko. In characteristic zero, our algebras are also closely related to work of Kook-Reiner-Stanton and Denham.

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Tom Braden, Carl Mautner. 2016-09-15. Matroidal Schur Algebras. https://arxiv.org/abs/1609.04507

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