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The flag major index and group actions on polynomial rings. (English) Zbl 1058.20031

Summary: A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type \(B\), it is equidistributed with length. For more general wreath products it appears in an explicit formula for the Hilbert series of the (diagonal action) invariant algebra.

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups
20P05 Probabilistic methods in group theory
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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