Reddit reviews Symmetric Functions and Hall Polynomials (Oxford Classic Texts in the Physical Sciences: Oxford Mathematical Mongraphs)
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Anything you want to know about symmetric functions and characters is probably in:
https://www.amazon.com/Symmetric-Functions-Polynomials-Physical-Sciences/dp/0198739125
This is also a popular text on the subject that starts from more of the basics of representation theory:
https://www.amazon.com/Representation-Symmetric-Encyclopedia-mathematics-applications/dp/0201135159/ref=sr_1_1?s=books&ie=UTF8&qid=1520448586&sr=1-1&keywords=James+and++Kerber+group