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2024 | OriginalPaper | Chapter

Specht Modules and Representations of Symmetric Group

Authors : Maha Oudah Alshammari, Faryad Ali

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

The symmetric group plays a key role in many areas of research in addition to mathematics and hence is of great importance. It is well known that representations of a symmetric group can be approached from three different directions: by using results from the general theory of group representations, by employing combinatorial techniques, or via symmetric functions. In this paper, we study the irreducible representations of symmetric groups by using the Specht Modules, which are irreducible sub-modules of the permutation modules. We provide a complete description of the construction of the irreducible representations via Young Symmetrizers (also called row and column stabilizers) and the Frobenius Formula. We explore a connection between Young Tableaux and the representation of the symmetric group \(S_n\). We describe the construction of Specht Modules \(S^\lambda \) for each partition \(\lambda \) of n.

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previous chapter Additivity of Multiplicative b-Generalized (Skew) Derivations
next chapter Commutativity Theorems on Prime Rings with Generalized Derivations
Literature
1.
Booher, J.: Representations of the symmetric group via Young tableaux (1931)
2.
Fulton, W.: Young Tableaux: With Applications to Representation Theory and Geometry. Cambridge University Press (1997)
3.
Fulton, W., Harris, J.: Representation Theory. Springer (2013)
4.
James, G., Liebeck, M.: Representations and Characters of Groups. Cambridge University Press(2001)
5.
Larsen, M., McCarthy, P.: Multiplicative Theory of Ideals. Academic Press (1971)
6.
Sagan, B.: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. Springer (2013)
7.
Saikia, M.: Representations of the Symmetric Group, International Centre for Theoretical Physics (2015)
8.
Serre, J.: Linear Representations of Finite Groups. Springer (1977)
9.
Zhao, Y.: Young Tableaux and the Representations of the Symmetric Group. The Harvard College Mathematics Review. Cambridge (2018)
10.
Zhou, J.: Lecture Notes for Course at Tsinghua University, CiteSeer (2003)
Metadata
Title
Specht Modules and Representations of Symmetric Group
Authors
Maha Oudah Alshammari
Faryad Ali
Copyright Year
2024
Book
Advances in Ring Theory and Applications

Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-50795-3_4

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