Major Indices and Perfect Bases for Complex Reflection Groups

2007/08/13 by Shwartz, Robert, Adin, Ron M., Roichman, Yuval
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0708.1675

Abstract

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.

Related

• Colored-Descent Representations of Complex Reflection Groups G(r,p,n)
• Basic Invariants of the Complex Reflection Group No.34 Constructed by Conway and Sloane
• Invariant theory for coincidental complex reflection groups
• A reduction theorem for good basic invariants of finite complex reflection groups
• Reflection Groups. A Contribution to the Handbook of Algebra