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

Kunle Adegoke^1, , 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

Cite this paper:
Kunle Adegoke, Olawanle Layeni, Rauf Giwa and Gbenga Olunloyo. The Standard Representation of the Symmetric Group S_n 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 S_n. 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.
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[4]	Wikipedia. Representation theory of the symmetric group http://en.wikipedia.org/wiki/Representation_theory_of_the_symmetric_group. 2015.