Irreducible Representations of Groups of Order 8

Authors

  • Nor Haniza Sarmin
  • Wan Heng Fong

DOI:

https://doi.org/10.11113/matematika.v22.n.177

Abstract

Irreducible representations of a group provide the ways for labelling orbitals, determining molecular orbitals formation and determining vibrational motions for a molecule. A set of irreducible representations represents the ways a particular bond, atom or sets of atoms may respond to a given set of symmetry operations. In this paper, the irreducible representations of all groups of order 8, namely $D_4$, $Q$, $C_8$, $C_2 \times C_4$ and $C_2 \times C_2 \times C_2$ are obtained using Burnside method and Great Orthogonality Theorem method. Then, comparisons of the two methods are made. Keywords: Irreducible representation; group; Burnside method; Great Orthogonality Theorem method.

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Published

2006-06-01

Issue

Section

Mathematics