Some characters that depend only on length

摘要

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.