| 1. | Then is a field if and only if is irreducible over.
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| 2. | This reducible representation is decomposed into the sum of irreducible representations.
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| 3. | These irreducible representations correspond to the symmetry of the orbitals involved.
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| 4. | However, more complex systems were still computationally irreducible and unpredictable.
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| 5. | However, an irreducible representation of may not be irreducible for.
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| 6. | However, an irreducible representation of may not be irreducible for.
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| 7. | It can be shown that the complement of P is irreducible.
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| 8. | Without space parity inversion, it is not an irreducible representation.
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| 9. | It is thus reducible with these two lines as irreducible components.
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| 10. | The dimension is extended additively to direct sums of irreducible bimodules.
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