The Representation Theory of the Symmetric Groups
Date
2015-03-23
Authors
Halverson-Duncan, Brittany
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Abstract
This paper forms an introductory account of the irreducible representations of the permutation group using Young Tableaux as the tool to achieve this. The basics of C*-Algebra theory and Young Tableaux are provided including a brief history of the two subjects. This paper provides a straightforward development of the subject up to the main result which says that restricting the irreducible representations of S_n corresponding to the Young diagrams of shape ? to S_n-1 decomposes as the direct sum of the irreducible representations of S_n-1 corresponding to the Young diagrams formed by removing one box from ?.
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Keywords
permutation group, Young Tableaux