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Oriented Lagrangian Matroids

โœ Scribed by Richard F. Booth; Alexandre V. Borovik; Israel M. Gelfand; Neil White

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
201 KB
Volume
22
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of connected components. The definitions are made first in terms of a combinatorial axiomatisation, and then again in terms of elementary geometric properties of the Coxeter matroid polytope. We also generalise the concept of rank and signature of a quadratic form to symplectic Lagrangian matroids in a surprisingly natural way.

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