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A Decomposition of Fl(n)d Indexed by Permutation Arrays

✍ Scribed by Kimmo Eriksson; Svante Linusson


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
137 KB
Volume
25
Category
Article
ISSN
0196-8858

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✦ Synopsis


We study a decomposition of Fl n d-1 , where Fl n denotes the flag manifold over n . The strata are defined by the dimensions of intersections of one space from each flag, so for d equal to 2 this is the usual Bruhat cell decomposition. The strata are indexed by "permutation arrays," which are d-dimensional analogs of permutation matrices. We present a partial order on these permutation arrays, specializing to the Bruhat order on S n when d equals 2 and to the lattice of partitions of a d-set when n equals 2.


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