Book recommendations for reading A. Okounkov and A. Vershik's approach for complex irreducible representations of symmetric groups? Does anybody have book recommendations for reading A. Okounkov and A. Vershik's approach for complex irreducible representations of symmetric groups?  Preferably, I am looking for a book that is intended for an undergraduate/first year graduate student who know basics of Representation theory.
 A: I am not aware of many books following the Okounkov-Vershik approach (which is a shame because it is way more enlightening, at least in some directions...). One option though is this book, Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras; you can tell by the title that it is exactly what you are looking for but I would warn you, it is not the easiest read...
The original paper is a bit dense to study but I guess that depends on your algebra background; these notes will help you if you decide to study from there a bit.
Another place to have a look, if you have access to it, is the book Graphs on Surfaces and their applications; read the appendix (by Zagier) on representation theory. Many libraries provide online access to the book, and Zagier manages to explain in a couple of pages the gist of what is going on in the Okounkov approach. At least you'll have a sort of roadmap for what's coming (the introduction of the original paper might seem a bit off-putting for all of us who lack Okounkov's and Vershik's insight).
