The set of dominance-minimal roots
Research Report 94-43
Date: 23 December 1994
If alpha and beta are positive roots in the root system of a Coxeter group W,
we say that alpha dominates beta if w(beta) is negative whenever w(alpha) is
negative for w in W. We say that alpha is elementary or dominance-minimal, if
it does not dominate any root other than itself. It has been shown that the
set of dominance-minimal roots is finite if W has finite rank, and this can
be used to show that W is automatic. To limit the size of the relevant automata,
and possibly facilitate other Coxeter group algorithms, we give an explicit
description of the set of elementary roots.
Coxeter group. dominance.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics