Reducible and irreducible representations

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Reducible and irreducible representations
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Outline

• Book 2, chapters 2.4-2.7, 3.1-3.3
• Representations
• Irreducible
• Reducible
• Character tables
• Reduction of reducible representations
• Inspection method
• Systematic method

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The concept of a representation
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Definition of a representation

• A representation of a group may be defined as a
  set of matrices, each corresponding to a single
  operation in the group, that can be combined
  among themselves similarly to how the group
  elements (symmetry operations) combine.
• The dimension of a representation is the order of
  the square matrices that constitute it.

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Representations in C2v
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Irreducible representations
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Character tables
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