Abstract/Details

Various methods for calculating reducible and irreducible representations of the symmetric group


2009 2009

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Abstract (summary)

Group Representation Theory has many uses in Physics and Chemistry, representations of the symmetric group being the most widely used. This thesis introduces Group Representation Theory and discusses various ways to calculate representations. The group most focused upon is the symmetric group. The first way to calculate representations of the symmetric group is by Young's natural representation which utilizes the fact that there is a one-to-one correspondence between Specht modules and the irreducible [special characters omitted]-modules. The second way is to decompose the group algebra [special characters omitted] and find the representations of it which are the same as the group representations. This method uses Young operators which are irreducible idempotents and generate certain invariant subalgebras. Another method involves inducing representation of [special characters omitted] from the known representation of [special characters omitted]. Numerous computations and examples are provided.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Various methods for calculating reducible and irreducible representations of the symmetric group
Author
Knight, Jason
Number of pages
61
Publication year
2009
Degree date
2009
School code
0390
Source
MAI 47/05M, Masters Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109135664
Advisor
Ablamowicz, Rafal
Committee member
Mills, Allan; Murdock, David
University/institution
Tennessee Technological University
Department
Mathematics
University location
United States -- Tennessee
Degree
M.S.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
1464217
ProQuest document ID
305068976
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305068976/fulltextPDF
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