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The action of a finite reflection group (type A) on its set of roots isunderstood as a permutation representation or group action. We show that thisrepresentation is an induced representation from a certain kind of parabolicsubgroup. Furthermore, we use this representation to define a statistic(derived from the length function) on the set of roots. A possible applicationto Costas Arrays is hinted at in a proposition.

A statistic on the roots of a finite reflection group and a correspondence between the height function and Bruhat order