Matroidal Schur Algebras

Tom Braden; Carl Mautner

Matroidal Schur Algebras

Representation Theory 2016-09-16 v1 Combinatorics

Authors: Tom Braden , Carl Mautner

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.

Keywords

matroid theory representation theory of algebras graded algebras

Cite

@article{arxiv.1609.04507,
  title  = {Matroidal Schur Algebras},
  author = {Tom Braden and Carl Mautner},
  journal= {arXiv preprint arXiv:1609.04507},
  year   = {2016}
}

Comments

22 pages

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