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Group Representation
Undergraduate
Definition
Homomorphism realizing group as group of invertible linear transformations on vector space
Formulas
ρ: G → GL(V)
ρ(gh) = ρ(g)ρ(h)
Degree = dim V
Examples
Example 1
Cyclic group representations
Example 2
Symmetric group Sₙ
Example 3
Trivial representation
Applications
Quantum mechanics
Chemistry
Physics
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