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Some Geometries Associated with Parabolic Representations of Groups of Lie Type

Published online by Cambridge University Press:  20 November 2018

Bruce N. Cooperstein
Bruce N. Cooperstein*
Affiliation:
University of California at Santa Cruz, Santa Cruz, California
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Suppose (P, △) is an undirected graph without loops or multiple edges. We will denote by △ (x) the vertices adjacent to x and . Let (G, P) be a transitive permutation representation of a group G in a, set P, and Δ be a non-trivial self-paired (i.e. symmetric) orbit for the action of G on P X P. We identify △ with the set of all two subsets ﹛x, y﹜ with (x, y) in △. Then we have a graph (P, Δ) with G ≦ Aut (P, △), transitive on both P and △.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1021 - 1031
Copyright
Copyright © Canadian Mathematical Society 1976

References

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