Abstract
Generic algebra methods are used to translate combinatorial results about Weyl groups into statements about classical groups. A consequence is the maximal nature of the rank of the incidence matrix of isotropice-subspaces vs isotropic f-subspaces of a finite vector space V with a form F, in many cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4,5,6. (Herman, Paris, 1968).
R. Carter, Simple Groups of Lie Type. (John Wiley & Sons, London, New York, Sydney, Toronto, 1972).
C.W. Curtis, N. Iwahori, R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with BN-pairs, I.H.E.S. Publ. Math. 40 (1971), 81–116.
P. Dembowski, Finite Geometries. (Springer-Verlag, Berlin, Heidelberg, New York, 1968).
W.M. Kantor, On incidence matrices of finite projective and affine spaces, Math. Z. 124 (1972), 315–318.
G.I. Lehrer, On incidence structures in finite classical groups, (to appear in Math. Zeit.).
R. Steinberg, Lectures on Chevalley Groups (lecture notes), Yale University, 1967.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
Lehrer, G.I. (1976). Some incidence structures of maximal rank. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097374
Download citation
DOI: https://doi.org/10.1007/BFb0097374
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08053-4
Online ISBN: 978-3-540-37537-1
eBook Packages: Springer Book Archive