The study of the symmetric groups forms one of the basic building
blocks of modern group theory. This book is the first completely
detailed and self-contained presentation of the wealth of
information now known on the projective representations of the
symmetric and alternating groups. Prerequisites are a basic
familiarity with the elementary theory of linear representations
and a modest background in modern algebra. The authors have taken
pains to ensure that all the relevant algebraic and combinatoric
tools are clearly explained in such a way as to make the book
suitable for graduate students and research workers. After the
pioneering work of Issai Schur, little progress was made for half a
century on projective representations, despite considerable
activity on the related topic of linear representations. However,
in the last twenty years important new advances have spurred
further research. This book develops both the early theory of Schur
and then describes the key advances that the subject has seen since
then. In particular the theory of Q-functions and skew Q-functions
is extensively covered which is central to the development of the
subject.
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