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) |
Keywords:
flag major indices; Coxeter elements; Weyl groups; equidistributions with length functions; wreath products; products of Coxeter generatorsReferences:
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