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Shellability of the Bruhat Order on Borel Orbit Closures

Involutions and fixed-point-free involutions arise naturally as representatives for certain Borel orbits in invertible matrices. Similarly, partial involutions and partial fixed-point-free involutions represent certain Borel orbits in matrices which are not necessarily invertible. Inclusion relations among Borel orbit closures induce a partial order on these discrete parameterizing sets. In this dissertation we investigate the associated order complex of these posets. In particular, we prove that the order complex of the Bruhat poset of Borel orbit closures is shellable in symmetric as well as skew-symmetric matrices. / acase@tulane.edu

  1. tulane:24273
Identiferoai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_24273
Date January 2013
ContributorsTwelbeck, Tim (Author), Can, Mahir (Thesis advisor)
PublisherTulane University
Source SetsTulane University
LanguageEnglish
Detected LanguageEnglish
Format98
RightsCopyright is in accordance with U.S. Copyright law

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