For SL(2n+1) with maximal parabolic M = sl(n+1) + sl(n), the paper lists elementary representation multiplets for n=1,2,3 and claims exhaustiveness without proof.
Langlands Problems in the theory of automorphic forms, Lect
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Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)
For SL(2n+1) with maximal parabolic M = sl(n+1) + sl(n), the paper lists elementary representation multiplets for n=1,2,3 and claims exhaustiveness without proof.