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representation theoryPlease help with right and specific explanation!I will give a like! Consider the subgroup AS of index 2,where A, is the alternating group and S, is the symmetric group.Viewed as a subgroup of Ss,As consists of the even permutations of S.The character table for S, is as follows: 11 10 20 30 24 15 20 Ss 1 (12) (123 1234 (12345) 1234 12345 1 1 1 1 1 1 1 1 -1 1 -1 1 1 -1 4 2 1 0 -1 0 -1 -2 1 0 -1 0 1 465 0 0 0 1 -2 0 -1 -1 0 1 1 7 5 -1 -1 1 0 1 -1 a Determine which of the irreducible representations of S, remain irreducible when restricted to As,and which ones split as a direct sum of multiple irreducible representations. Use this to construct the character table for A (b For each irreducible representation U of As,decompose IndU into a direct sum of irreducible S,-representations Hint:Use Frobenius Reciprocity.

          representation theoryPlease help with right and specific explanation!I will give a like!
Consider the subgroup AS of index 2,where A, is the alternating group and S, is the symmetric group.Viewed as a subgroup of Ss,As consists of the even permutations of S.The character table for S, is as follows:
11 10 20 30 24 15 20 Ss 1 (12) (123 1234 (12345) 1234 12345 1 1 1 1 1 1 1 1 -1 1 -1 1 1 -1 4 2 1 0 -1 0 -1 -2 1 0 -1 0 1 465 0 0 0 1 -2 0 -1 -1 0 1 1 7 5 -1 -1 1 0 1 -1
a Determine which of the irreducible representations of S, remain irreducible when restricted to As,and which ones split as a direct sum of multiple irreducible representations. Use this to construct the character table for A (b For each irreducible representation U of As,decompose IndU into a direct sum of irreducible S,-representations Hint:Use Frobenius Reciprocity.

representation theoryplease help with right and specific explanationi will give a like consider the subgroup as of index 2where a is the alternating group and s is the symmetric groupviewed 07609

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