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Generalized Foulkes' Conjecture and tableaux construction

Citation

Vessenes, Rebecca Angel (2004) Generalized Foulkes' Conjecture and tableaux construction. Dissertation (Ph.D.), California Institute of Technology. http://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 $1_{Sym{b}wrSym{a}}^{Sym{n}}$ occurs with greater or equal multiplicity in $1_{Sym{a}wrSym{b}}^{Sym{n}}$. We generalize part of this to say those irreducibles also occur in $1_{Sym{d}wrSym{c}}^{Sym{n}}$, 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 $Sym{b}wrSym{a}$ modules and in doing so, completely classify all such tableaux for a=2 and a=3.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:symmetric group; wreath product
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wales, David B.
Thesis Committee:
  • Wales, David B. (chair)
  • Chan, Ada
  • Ramakrishnan, Dinakar
  • Aschbacher, Michael
  • Wilson, Richard M.
Defense Date:29 April 2004
Record Number:CaltechETD:etd-05192004-121256
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05192004-121256
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1870
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:28 May 2004
Last Modified:26 Dec 2012 02:43

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