139 research outputs found
Upper bounds for eigenvalue multiplicities of almost cyclic elements in irreducible representations of simple algebraic groups
We study the irreducible representations of simple algebraic groups in which
some non-central semisimple element has at most one eigenvalue of multiplicity
greater than 1. We bound the multiplicity of this eigenvalue in terms of the
rank of the group.Comment: 1 figur
Large dimensional classical groups and linear spaces
Suppose that a group has socle a simple large-rank classical group.
Suppose furthermore that acts transitively on the set of lines of a linear
space . We prove that, provided has dimension at least 25,
then acts transitively on the set of flags of and hence the
action is known. For particular families of classical groups our results hold
for dimension smaller than 25.
The group theoretic methods used to prove the result (described in Section 3)
are robust and general and are likely to have wider application in the study of
almost simple groups acting on finite linear spaces.Comment: 32 pages. Version 2 has a new format that includes less repetition.
It also proves a slightly stronger result; with the addition of our
"Concluding Remarks" section the result holds for dimension at least 2
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