Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2015, 3(5), 126-127
DOI: 10.12691/tjant-3-5-3
Open AccessArticle

The Standard Representation of the Symmetric Group Sn over the Ring of Integers

Kunle Adegoke1, , Olawanle Layeni2, Rauf Giwa1 and Gbenga Olunloyo1

1Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife, Nigeria

2Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria

Pub. Date: December 14, 2015

Cite this paper:
Kunle Adegoke, Olawanle Layeni, Rauf Giwa and Gbenga Olunloyo. The Standard Representation of the Symmetric Group Sn over the Ring of Integers. Turkish Journal of Analysis and Number Theory. 2015; 3(5):126-127. doi: 10.12691/tjant-3-5-3

Abstract

In this paper we give a Casimir Invariant for the Symmetric group Sn. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of the permutation representation.

Keywords:
standard representation symmetric group casimir invariant

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References:

[1]  M. Hamermesh. Group Theory and Its Application to Physical Problems. Dover Publications, 1989.
 
[2]  W. Burnside. Theory of groups of finite order. Dover Publications, 1955.
 
[3]  W. Fulton and J. Harris. Representation theory. A first course,. Springer-Verlag, 1991.
 
[4]  Wikipedia. Representation theory of the symmetric group http://en.wikipedia.org/wiki/Representation_theory_of_the_symmetric_group. 2015.