# Why are they called Specht Modules?

I know that the simple modules of $\mathbb{C}S_n$ are called Specht Modules, and they are named after the German Mathematician Wilhelm Specht because he studied them, but I think these modules were studied before him, for example by Frobenius.

Could any one please tell me what is the Specht's contribution to this area that made people name these modules after him?

**I was reluctant about asking this question here or in MathsStackExchange, but finally I posted it here, if you think it is too naive to be here, please let me know I will happily move it to there.

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I personally think the question is fine. It's specific, and topic of interest to research mathematicians. –  Ben Webster Feb 17 at 23:36

The question is interesting though perhaps not strictly "research-level". Terminology in mathematics develops a bit haphazardly, and sometimes things get misleading names. In this case the work of Specht around 1935 did place the representations of symmetric groups in the then-modern setting of module theory. But the notion of "Specht module" seems to have emerged around 1970 in the rapidly developing work on representations of the groups in prime characteristic. Work of M.H. Peel and especially work of Gordon James popularized the notion. In particular, James exploited the fact that the characteristic 0 Specht modules have a fairly natural reduction mod $p$ for any prime $p$. This is somewhat analogous to the algebraic group situation, where "Weyl modules" come by such reductions and then have a unique distinguished composition factor.