First Sentence:
The theory of group representation provides the natural mathematical language for describing symmetries of the physical world.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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induced representation method, irreducible symmetrizers, general tensor space, rearrangement lemma, irreducible basis vectors, group multiplication rule, general basis vector, irreducible representation matrices, invariant integration measure, vertical permutations, group parameter space, undotted indices, tensorial method, helicity formalism, tensor subspaces, dotted index, space inversion symmetry, parity eigenvalue, abelian invariant subgroup, angular momentum basis, irreducible operators, inequivalent irreducible representations, unitary irreducible representations, time reversal transformation, irreducible invariant subspaces
Key Phrases - Capitalized Phrases (CAPs):
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Schur's Lemma, Correspondence Principle, Dirac Equation
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