Studying Langlands's classification of irreducible admissible representations, I have been rather stunned by the following:
Theorem Up to infinitesimal equivalence, all irreducible admissible representations of $\text{GL}(n,\mathbb{R})$ are the unique irreducible quotient of parabolically induced representations of Levi subgroups isomorphic to products of $\text{GL}(2,\mathbb{R})$ and $\text{GL}(1,\mathbb{R})$.
Which follows from section 4 of his paper ON THE CLASSIFICATION OF IRREDUCIBLE REPRESENTATIONS OF REAL ALGEBRAIC GROUPS, as is pointed out for example in Knapp's article about the Archimedean case of the local Langlands correspondence in the Motives proceedings, where one can find a more precise statement on page 8 of the pdf.
My first and main question: are there any good reasons this should be intuitive?
(As an aside, it is my understanding that this was not known before Langlands work, but please correct me if I am wrong about this. If I am indeed correct, was this in any way expected?)
I find it difficult to see why this is intuitive for several reasons:
First of all, this is a phenomenon which starts at $\text{GL}(3,\mathbb{R})$, but the main introductory sources on representation theory stop themselves at giving a complete description of all irreducible admissible representations up to infinitesimal equivalence at $n=2$.
Secondly, this seems somewhat a "real" phenomenon: if I am not mistaken, over the p-adic numbers there are supercuspidal representations of $\text{GL}(n,\mathbb{Q}_{p})$, which are really new to the group, and not induced from Levis.
Does the situation change drastically if I do not take only admissible representations? So, is this assumption the culprit? Or is it the fact that I am taking them only up to infinitesimal equivalence? Not only I have no idea about this, but I cannot find anything in the literature which delves deeper in these two possible directions.
As $L$-packets of irreducible representations should be in correspondence with automorphic $L$-functions, and $L$-packets for $\text{GL}(n,\mathbb{R})$ contain only one infinitesimal equivalence class, perhaps the intution for this result comes from a good knowledge of automorphic $L$-functions. Unfortunately, this is another hole in my background.
But perhaps this statement is intuitive to some expert in the field. Unfortunately, I do not know any of them directly and hence here I am.
I think that this question may be useful to others for several reasons: first, it further publicizes a somewhat unintuive result about objects of great importance; secondly, a good answer would yield light either on the structure of irreducible representations of $\text{GL}(n,\mathbb{R})$ or on the somewhat technical conditions imposed on irreducible representations of real reductive groups in the Langlands correspondence, or perhaps even on the historical context.
My background: I have a good knowledge of real Lie groups, say on the level of Knapp's book "Beyond an introduction" and a major interest in the Langlands program. Unfortunately, going through the fourth section of Langlands paper is impossible for me at the moment, as it is not part of my current research and would take up too much time, if even possible at all.
The possible requisites for a good answer would be: address the main question and explain why (to you or somebody else) this is nearly obvious, or very expected; In case this was not possible, say why and address one or several of the above 4 reasons I listed above; bonus points for whoever can also tell me whether this was known or conjectured before Langlands.
My motivation: astonishment, and the curiosity which followed it.
