Boundaries of Coxeter Matroids |
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Authors: | Alexandre V. Borovik Israel Gelfand Neil White |
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Affiliation: | aDepartment of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, United Kingdom;bDepartment of Mathematics, Rutgers University, New Brunswick, New Jersey, 08903;cDepartment of Mathematics, University of Florida, Gainesville, Florida, 32611 |
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Abstract: | The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQiofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3). |
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