| 31. | By taking Kronecker products of with itself repeatedly, one may construct all higher irreducible representations.
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| 32. | If G is a characters of the irreducible representations are given by the Weyl character formula.
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| 33. | The dimensions of irreducible representations 1, 3, 3, 6, 7, 8.
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| 34. | As a simple corollary, every complex irreducible representation of Abelian groups is one-dimensional.
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| 35. | In the field of support of the regular representation is the whole space of irreducible representations.
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| 36. | Rather, one requires a core whose symmetry group admits a two-dimensional irreducible representation.
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| 37. | A given irreducible representation V of G is contained n times in the regular representation.
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| 38. | The alternating groups for have only one one-dimensional irreducible representation, the trivial representation.
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| 39. | This sum can help narrow down the dimensions of the irreducible representations in a character table.
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| 40. | Almost any irreducible representation is generic.
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