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I'm looking for a nice book that discusses the representation theory of the symmetric group.

My background is an introductory class in representation theory.

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  • $\begingroup$ Lederman's "Introduction to group characters" has an account of the characters of the symmetric group (working over $\mathbb C$) $\endgroup$ – Mark Bennet Oct 18 '14 at 8:46
  • $\begingroup$ Fulton & Harris is not always exactly to my taste, but it is a common reference book here, and does cover the symmetric groups to the level of detail that satisfied me. If you don't like Lie group stuff, then you probably should not buy it. University libraries are your friends. $\endgroup$ – Jyrki Lahtonen Oct 18 '14 at 8:47
  • $\begingroup$ James' Springer lecture notes and James-Kerber book is the usual recommended reference; but one may not like it because they discuss methods from decades ago. Mathas book on Iwahori-Hecke algebra is also good but computational heavy, in that sense, it may be "too explicit" for people. I personally like Kleshchev lecture notes, there are several versions depending on which direction (purely representation and homological within the realm of symmetric group, or more into generalisation to Hecke and KLR algebras). $\endgroup$ – Aaron Oct 18 '14 at 14:47
  • $\begingroup$ There are also Segal's book - also the classical approach to Specht modules like James-Kerber. Okuonkov-Vershik have a book on their approach to symmetric group, which differ slightly from the James-Kerber school approach, but enlightened many modern approach to KLR algebras, also used by Mathas and Kleshchev. $\endgroup$ – Aaron Oct 18 '14 at 14:50
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Bruce Sagan's "The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions" is probably exactly what you are looking for. It covers basic representation theory but quickly moves into the representation theory of the symmetric group.

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