Generalized Foulkes' Conjecture and Tableaux Construction

Author: Vessenes, Rebecca Angel

Year: 2004

Degree: Dissertation (Ph.D.)

Advisor: Wales, David B.

Committee Members: Wales, David B.; Chan, Ada; Ramakrishnan, Dinakar; Aschbacher, Michael; Wilson, Richard M.

Option: Mathematics

DOI: 10.7907/4C12-SV65

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.

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• AppendixA.pdf (application/pdf)
• Chapter1.pdf (application/pdf)
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• Chapter11and12.pdf (application/pdf)
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