Lagrangian Pairs and Lagrangian Orthogonal Matroids

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dc.creatorBooth, Richard F.
dc.creatorBorovik, Alexandre V.
dc.creatorWhite, Neil
dc.date2002-09-09
dc.date.accessioned2026-07-07T04:50:43Z
dc.date.available2026-07-07T04:50:43Z
dc.descriptionRepresented Coxeter matroids of types $C_n$ and $D_n$, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type $C_n$ and $D_n$, respectively. Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally isotropic subspaces. There are also buildings of type $B_n$ arising from flags of totally isotropic subspaces in odd-dimensional orthogonal space. Coxeter matroids of type $B_n$ are the same as those of type $C_n$ (since they depend only upon the reflection group, not the root system). However, buildings of type $B_n$ are distinct from those of the other types. The matroids representable in odd dimensional orthogonal space (and therefore in the building of type $B_n$) turn out to be a special case of symplectic (flag) matroids, those whose top component, or Lagrangian matroid, is a union of two Lagrangian orthogonal matroids. These two matroids are called a Lagrangian pair, and they are the combinatorial manifestation of the ``fork'' at the top of an oriflamme (or of the fork at the end of the Coxeter diagram of $D_n$). Here we give a number of equivalent characterizations of Lagrangian pairs, and prove some rather strong properties of them.
dc.descriptionRequires amssymb.sty; 12 pages, 2 LaTeX figures
dc.identifierhttps://arxiv.org/abs/math/0209100
dc.identifierhttp://arxiv.org/abs/math/0209100
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64891
dc.subjectCombinatorics
dc.subject05B35
dc.titleLagrangian Pairs and Lagrangian Orthogonal Matroids
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