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Aug 15, 2017 at 18:23 comment added Anton Mellit Sorry, I should have made it more explicit. It is known that irreducible modules of $U(n)$ are precisely the Schur functors applied to the standard representation. That's why these are irreducible modules.
Aug 14, 2017 at 9:54 comment added Han Jin Ma Thanks for the great answer! Just to be sure I understand what's happening, in the last displayed equation, is it clear that each of the summands are irreducible modules? If they're not irreducible then I don't understand why Taking invariants we see that only terms with $\lambda = \mu$ survive,
Aug 12, 2017 at 16:23 vote accept Han Jin Ma
Aug 12, 2017 at 16:23 history bounty ended Han Jin Ma
Aug 12, 2017 at 16:23 vote accept Han Jin Ma
Aug 12, 2017 at 16:23
Aug 12, 2017 at 16:23 vote accept Han Jin Ma
Aug 12, 2017 at 16:23
Aug 12, 2017 at 16:21 vote accept Han Jin Ma
Aug 12, 2017 at 16:23
Aug 12, 2017 at 16:21 vote accept Han Jin Ma
Aug 12, 2017 at 16:21
Aug 11, 2017 at 15:26 history answered Anton Mellit CC BY-SA 3.0