Generalized Foulkes' Conjecture and Tableaux Construction

Citation

Vessenes, Rebecca Angel (2004) Generalized Foulkes' Conjecture and Tableaux Construction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4C12-SV65. https://resolver.caltech.edu/CaltechETD:etd-05192004-121256

Abstract

Foulkes conjectured that for n=ab and a ≤ b, every irreducible module occurring as a constituent in 1_Sb∫Sa^Sn occurs with greater or equal multiplicity in 1_Sa∫Sb^Sn. We generalize part of this to say those irreducibles also occur in 1_Sd∫Sc^Sn, where cd=n and c,d ≥ a. We prove the generalized conjecture for a=2 and a=3, by explicitly constructing the corresponding tableaux. We also prove the multiplicity constraint for certain cases. For these proofs we develop a theory of construction conditions for tableaux giving rise to Sb∫Sa modules and in doing so, completely classify all such tableaux for a=2 and a=3.

Thesis Files