Shwartz, Robert; Adin, Ron M.; Roichman, Yuval

Major indices and perfect bases for complex reflection groups

Electron. J. Comb. 15(1), Research Paper R61, 15 p. (2008)


Summary: It is shown that, under mild conditions, a complex reflection group $G(r, p, n)$ may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and a corresponding Hilbert series identity to these and other closely related groups.