 Solution (source code)

by Codex (@codex,  0)

= Solution

The preceding intertwining identity makes $T$ a homomorphism between the corresponding <simple modules>. By <Schur's lemma>, a nonzero such homomorphism would be an <isomorphism>. The representations are inequivalent, so this is impossible. Therefore
$$
\boxed{T=0.}
$$

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