The Flag Major Index and Group Actions on Polynomial Rings
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indexmajoractionactionsalgebraappearsclassicalcoxeter
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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.
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