Academic Bibliography

 Search 200 years of publications by Ghent University researchers.
Advanced search
2 files | 1.06 MB
Add to list
  1. Search results
  2. On the generating rank and embedding ...

On the generating rank and embedding rank of the hexagonic Lie incidence geometries

A. De Schepper, Jeroen Schillewaert (UGent) and Hendrik Van Maldeghem (UGent)
(2024) COMBINATORICA. 44(2). p.355-392
Author
Organization
Project
Abstract
Given a (thick) irreducible spherical building Omega, we establish a bound on the difference between the generating rank and the embedding rank of its long root geometry and the dimension of the correspondingWeyl module, by showing that this difference does not grow when taking certain residues of Omega (in particular the residue of a vertex corresponding to a point of the long root geometry, but also other types of vertices occur). We apply this to the finite case to obtain new results on the generating rank of mainly the exceptional long root geometries, answering an open question by Cooperstein about the generating ranks of the exceptional long root subgroup geometries. We completely settle the finite case for long root geometries of type An, and the case of type F-4,F-4 over any field with characteristic distinct from 2 (which is not a long root subgroup geometry, but a hexagonic geometry).
Keywords
Embedding rank, Generating rank, Lie incidence geometry, Long root subgroup geometry, Exceptional geometries, SPACES, MODULE

Downloads

  • Download
    (...).pdf
    • full text (Published version)
    • |
    • UGent only
    • |
    • PDF
    • |
    • 612.03 KB
  • Download
    01HW5NM4RF1HRDB26BYG8FTHKR.pdf
    • full text (Accepted manuscript)
    • |
    • open access
    • |
    • PDF
    • |
    • 449.95 KB

Citation

Please use this url to cite or link to this publication:

MLA
De Schepper, A., et al. “On the Generating Rank and Embedding Rank of the Hexagonic Lie Incidence Geometries.” COMBINATORICA, vol. 44, no. 2, 2024, pp. 355–92, doi:10.1007/s00493-023-00075-y.
APA
De Schepper, A., Schillewaert, J., & Van Maldeghem, H. (2024). On the generating rank and embedding rank of the hexagonic Lie incidence geometries. COMBINATORICA, 44(2), 355–392. https://doi.org/10.1007/s00493-023-00075-y
Chicago author-date
De Schepper, A., Jeroen Schillewaert, and Hendrik Van Maldeghem. 2024. “On the Generating Rank and Embedding Rank of the Hexagonic Lie Incidence Geometries.” COMBINATORICA 44 (2): 355–92. https://doi.org/10.1007/s00493-023-00075-y.
Chicago author-date (all authors)
De Schepper, A., Jeroen Schillewaert, and Hendrik Van Maldeghem. 2024. “On the Generating Rank and Embedding Rank of the Hexagonic Lie Incidence Geometries.” COMBINATORICA 44 (2): 355–392. doi:10.1007/s00493-023-00075-y.
Vancouver
1.
De Schepper A, Schillewaert J, Van Maldeghem H. On the generating rank and embedding rank of the hexagonic Lie incidence geometries. COMBINATORICA. 2024;44(2):355–92.
IEEE
[1]
A. De Schepper, J. Schillewaert, and H. Van Maldeghem, “On the generating rank and embedding rank of the hexagonic Lie incidence geometries,” COMBINATORICA, vol. 44, no. 2, pp. 355–392, 2024.
@article{01HW5NM4RF1HRDB26BYG8FTHKR,
  abstract     = {{Given a (thick) irreducible spherical building Omega, we establish a bound on the difference between the generating rank and the embedding rank of its long root geometry and the dimension of the correspondingWeyl module, by showing that this difference does not grow when taking certain residues of Omega (in particular the residue of a vertex corresponding to a point of the long root geometry, but also other types of vertices occur). We apply this to the finite case to obtain new results on the generating rank of mainly the exceptional long root geometries, answering an open question by Cooperstein about the generating ranks of the exceptional long root subgroup geometries. We completely settle the finite case for long root geometries of type An, and the case of type F-4,F-4 over any field with characteristic distinct from 2 (which is not a long root subgroup geometry, but a hexagonic geometry).}},
  author       = {{De Schepper, A. and Schillewaert, Jeroen and Van Maldeghem, Hendrik}},
  issn         = {{0209-9683}},
  journal      = {{COMBINATORICA}},
  keywords     = {{Embedding rank,Generating rank,Lie incidence geometry,Long root subgroup geometry,Exceptional geometries,SPACES,MODULE}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{355--392}},
  title        = {{On the generating rank and embedding rank of the hexagonic Lie incidence geometries}},
  url          = {{http://doi.org/10.1007/s00493-023-00075-y}},
  volume       = {{44}},
  year         = {{2024}},
}
Altmetric
View in Altmetric
Web of Science
Times cited: