The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions

This text is an introduction to the representation theory of the symme tric group from three different points of view: via general representa tion theory, via combinatorial algorithms, and via symmetric functions . It is the only book to deal with all three aspects of this subject a t once. The style of presentation is relaxed yet rigorous and the prer equisites have been kept to a minimum, undergraduate courses in linear algebra and group theory will suffice. And this is a very active area of current research, so the text will appeal to graduate students and mathematicians in other specialties interested in finding out about t his field. On the other hand, a number of the combinatorial results pr esented have never appeared in book form before and so the volume will serve as a good reference for teachers already working in this area. Among these results are Haiman's theory of dual equivalence and the be autiful Novelli-Pak-Stoyanovskii proof of the hook formula (the latter being new to the second edition).