The literature on the representation theory of the symmetric group contains some terminology that I find puzzling, and I am wondering if someone here knows the full story.
One of the standard ways to construct the irreducible representations of the symmetric group is to define Specht modules. This construction produces an explicit basis for the modules. If one now writes down the representing matrices with respect to this basis, the result is often referred to as Young's natural representation.
From a modern point of view at least, this terminology seems a little strange because it attributes "the same thing" to both Specht and Young. Now one possible explanation is that when Specht and Young were working on this stuff, it didn't seem like the same thing, and it's only today that they look the same. Indeed, in Specht's paper, he writes:
Zwischen den Youngschen Arbeiten und der vorliegenden bestehen daher kaum irgendwelche Zusammenhaenge ausser den rein ausserlichen, die darauf beruhen, dass die hier verwendeten kombinatorischen Hilfsmittel haufig auch von Herrn A. Young, freilich zu ganz anderen Zwecken herangezogen werden.
My German is poor but I think this translates to:
Between Young's work and the present work there exist hardly any connections except the purely superficial one that the combinatorial tools used here are also used by Mr. A. Young, albeit for entirely different purposes.
I tried to look up Young's papers, but found them daunting, and in particular I could not immediately locate anything that looked like "Young's natural representation." Apparently I'm not the only one who is daunted by Young's papers, because here's a quote from some lecture notes of G. D. James:
The representation theory of the symmetric groups was first studied by Frobenius and Schur, and then developed in a long series of papers by Young. Although a detailed study of Young's work would undoubtedly pay dividends, anyone who has attempted this will realize just how difficult it is to read his papers. The author, for one, has never undertaken this task, and so no reference will be found here to any of Young's proofs, although it is probable that some of the techniques presented here are identical to his.
So my question is, can someone point specifically to a place in Young's papers where he discussed what we would nowadays call "Young's natural representation"? And does anyone know the history of how the term "Young's natural representation" came to have its current meaning?