| 41. | The character of an irreducible representation V of a compact connected Lie group G is given by
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| 42. | The corresponding irreducible representations are the " fundamental representations " of the Lie group.
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| 43. | The Casimir element acts on any irreducible representation as multiplication by some complex scalar ? 2.
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| 44. | Where each is an irreducible representation.
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| 45. | They are called different irreducible representations of the \ operatorname { SU } ( 2 ) algebra.
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| 46. | The holonomy is labelled by a half integer N / 2 according to the irreducible representation used.
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| 47. | Such representations, amongst irreducible representations, can be picked out by the Frobenius-Schur indicator.
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| 48. | If H is an irreducible representation of the algebra of observables then the rays induce pure states.
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| 49. | The character of the corresponding irreducible representation ? "'f "'is given by
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| 50. | By Schur's lemma, this will be a multiple of the identity for irreducible representations.
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