Foulkes characters for complex reflection groups

@inproceedings{Miller2015FoulkesCF,
  title={Foulkes characters for complex reflection groups},
  author={Alexander R. Miller},
  year={2015}
}
Foulkes discovered a marvelous set of characters for the symmetric group by summing Specht modules of certain ribbon shapes according to height. These characters have many remarkable properties and have been the subject of many investigations, including a recent one [2] by Diaconis and Fulman, which established some new formulas, a conjecture of Isaacs, and a connection with Eulerian idempotents. We widen our consideration to complex reflection groups and find ourselves equipped from the start… 
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References

SHOWING 1-10 OF 16 REFERENCES
Foulkes characters, Eulerian idempotents, and an amazing matrix
John Holte (Am. Math. Mon. 104:138–149, 1997) introduced a family of “amazing matrices” which give the transition probabilities of “carries” when adding a list of numbers. It was subsequently shown
Permutation Statistics of Indexed Permutations
TLDR
The definitions of descent, excedance, major index, inversion index and Denert's statistics for the elements of the symmetric group Ld are generalized to indexed permutation, i.e. the elementsOf the group Snd are shown to be equidistributed over Snd.
The sign representation for Shephard groups
Abstract. Shephard groups are unitary reflection groups arising as the symmetries of regular complex polytopes. For a Shephard group, we identify the representation carried by the principal ideal in
Arrangements defined by unitary reflection groups
Let V be a complex vector space of dimension I. An arrangement in V is a finite set d of hyperplanes, all containing the origin. Let L = L ( d ) be the set of intersections of elements of ~r
Noncommutative symmetric functions and an amazing matrix
Finite Unitary Reflection Groups
Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of
Opérations sur l'homologie cyclique des algèbres commutatives
Le but essentiel de cet article est d'6tudier une filtration naturelle de l'homologie de Hochschild et de l'homologie cyclique des alg6bres commutatives. La m6thode employ6e consiste fi construire
...
...