Minimal and maximal constituents of twisted Foulkes characters
arXiv:1409.6879 · doi:10.1112/jlms/jdv070
Abstract
We prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric group that generalize Foulkes permutation characters. Restated in the language of symmetric functions, our results determine all minimal and maximal partitions that label Schur functions appearing in the plethysms s_ν\circ s_(m). As a corollary we prove two conjectures of Agaoka on the lexicographically least constituents of the plethysms s_ν\circ s_(m) and s_ν\circ s_(1^m).
23 pages