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.