I am trying to understand the Langlands classification. To that end, I am trying to find how I could deduce the Bernstein-Zelevinsky classifcation from the second description of the Langlands classification provided in the Wikipedia site https://en.wikipedia.org/wiki/Langlands_classification (I know there are better sources for this, but honestly this is the one that seems most readable to me). The fact that a partition corresponds to a parabolic seems obvious, but how do we get the second partition of the Bernstein Zelevinsky classification from the homomorphism a?


In the book New Developments in Lie Theory and Their Applications

published by Progress in Math by Tirao-Wallach check the article

Analytic and Geometric Realization of Representations by Wilfried Schmid

might be useful to you.

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    $\begingroup$ It is a useful source in general, thank you for the comment. But it still does not have an explicit workout for the Langlands correspondance, even for example in the GL2(Qp) case, which would be really helpful to me at this point. I know the classification of representations for this group, I just dont understand how they come up in the Langlands correspondance. $\endgroup$ – Ioannis Zolas Jun 19 '18 at 19:13

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