4. Plethysm for S3. Let (3), (1, 1, 1), and (2, 1) be the trivial, alternating, and standard represen- tations of S3. (a) Consider the permutational representation V ~ (3) @ (2, 1). Decompose AV into irre- ducibles. (b) Decompose S' (2, 1) and SB (2, 1) into irreducibles. (c) Decompose the regular representation R into irreducibles. (d) Prove that Sk+6(2, 1) ~ S" (2, 1) OR. Compute S" (2, 1) for all k