Group representation theory MOC

Representation theory of symmetric groups

The representation theory of symmetric groups is fundamental to group representation theory as a whole by virtue of Cayley’s theorem.

Representations

• 1-dimensional irreps of a finite symmetric group
• Characters of a finite symmetric group are real
• Associate representation
• Trivial and alternating characters of a finite symmetric group in tensor product decomposition

Group ring

• Symmetrizer and antisymmetrizer elements
• Young operator

Young operators

• Numeric partition, Young diagram, Young tableau
• Young operator

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