A Decomposition of Fl(n)d Indexed by Permutation Arrays
β Scribed by Kimmo Eriksson; Svante Linusson
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 137 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0196-8858
No coin nor oath required. For personal study only.
β¦ 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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