A decomposition of Fl(n)(d) indexed by permutation arrays
2000 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 25, no 2, 212-227 p.Article in journal (Refereed) Published
We study a decomposition of Fl(n)(d-1), where: Fl(n) denotes the flag manifold over C-n. The strata are defined by the dimensions of intersections of one space from each fag, 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.
Place, publisher, year, edition, pages
2000. Vol. 25, no 2, 212-227 p.
complete flag, flag manifold, permutation, permutation array, Bruhat order, partition lattice
IdentifiersURN: urn:nbn:se:kth:diva-20018ISI: 000089174400004OAI: oai:DiVA.org:kth-20018DiVA: diva2:338711
QC 201005252010-08-102010-08-10Bibliographically approved