Representatives of elliptic Weyl group elements in algebraic groups

Details Representatives of elliptic Weyl group elements in algebraic groups Representatives of elliptic Weyl group elements in algebraic groups

2011-09-26

arxiv.org/abs/1109.5487v1

Mathematics

Group Theory

20 pages

Scientific paper

An element w of a Weyl group W is called elliptic if it has no eigenvalue 1
in the standard reflection representation. We determine the order of any
representative g in a semisimple algebraic group G of an elliptic element w in
the corresponding Weyl group W. In particular if w has order d and G is simple
of type different from C_n or F_4, then g has order d in G.

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