ON THE COMPUTATION OF CHARACTER TABLES FOR SOME SYMMETRIC GROUPS Sn, n = 3,4 and 5
OBI MARTIN
Department of Mathematics, Federal University of Technology Owerri, Nigeria.
C. NOMETA IKENNA
Department of Mathematics, Federal University of Technology Owerri, Nigeria.
C. AZUBUIKE HENRY *
Department of Mathematics, Federal University of Technology Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This work presented the table of characters and irreducible character tables for the representation of some symmetric groups Sn, n = 3,4 and 5. The Frobenius and Hooklenght formula according to the work of Zhao (2008) was used in the computation of the character table for Sn, n = 3,4. It was observed that the formula becomes inefficient and cumbersome to use as n increases. Hence we showed that it will be more efficient to employ the help of a Computer Algebra System (we used GAP) [1] in computing the character table for Sn as n increases.
Keywords: Young tableau, character table, tabloids, permutation module, Specht modules