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Splitting fields and irreducible representations.

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Classify the irreducible representations of A_4 (wich as we know happen to be the even permutations of the alternating group) over R and over C. What is the splitting field for A_4.

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Splitting fields and irreducible representations are investigated and discussed. The solution is detailed and well presented.

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Mathematics, Other
Year 4

splitting fields and representations

Classify the irreducible representations of A4 (which as we know happen to be the even permutations of the alternating group) over R and over C. What is the splitting field for A4.

Solution: G = A4, the alternating group of 4 letters, has order 12, ie, |G| = 12. We know ...

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