The set of dominance-minimal roots


Brigitte Brink


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.

Key phrases

Coxeter group. dominance.

AMS Subject Classification (1991)

Primary: 20F55


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