Some characters that depend only on length

The author recently introduced Foulkes characters for a wide variety of reflection groups, and the hyperoctahedral ones have attracted some special attention. Diaconis and Fulman connected them to adding random numbers in balanced ternary and other number systems that minimize carries, and Goldstein, Guralnick, and Rains observed experimentally that they also play the role of irreducibles among the hyperoctahedral characters that depend only on length. We prove this conjecture and show that the same is true for a more general family of reflection groups.

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Received 19 August 2014

Accepted 9 June 2015

Published 1 September 2017