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THE PERMUTATION MODULES FOR GL(n+1, [ ]q) ACTING ON ℙn([ ]q) AND [ ]n+1q

Published online by Cambridge University Press:  01 February 2000

MATTHEW BARDOE  and
PETER SIN
MATTHEW BARDOE
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
PETER SIN
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA sin@math.ufl.edu
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Abstract

The paper studies the permutation representations of a finite general linear group, first on finite projective space and then on the set of vectors of its standard module. In both cases the submodule lattices of the permutation modules are determined. In the case of projective space, the result leads to the solution of certain incidence problems in finite projective geometry, generalizing the rank formula of Hamada. In the other case, the results yield as a corollary the submodule structure of certain symmetric powers of the standard module for the finite general linear group, from which one obtains the submodule structure of all symmetric powers of the standard module of the ambient algebraic group.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 58 - 80
Copyright
The London Mathematical Society 2000

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Footnotes

Research supported in part by NSF grant DMS9701065.