| Type of Document |
Dissertation |
| Author |
Vessenes, Rebecca Angel
|
| URN |
etd-05192004-121256 |
| Persistent URL |
http://resolver.caltech.edu/CaltechETD:etd-05192004-121256 |
| Title |
Generalized Foulkes' Conjecture and tableaux construction |
| Degree |
PhD |
| Option |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| David B. Wales |
Committee Chair |
| Ada Chan |
Committee Member |
| Dinakar Ramakrishnan |
Committee Member |
| Michael Aschbacher |
Committee Member |
| Richard Wilson |
Committee Member |
|
| Keywords |
- symmetric group
- wreath product
|
| Date of Defense |
2004-04-29 |
| Availability |
unrestricted |
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.
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Chapter8.pdf |
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CV.pdf |
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FullThesis.pdf |
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TableOfContents.pdf |
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