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

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

2008-03-06

arxiv.org/abs/0803.0782v4

Mathematics

Combinatorics

Scientific paper

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

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