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Projective Representations of the Symmetric Groups

Q-Functions and Shifted Tableaux

By: J. F. Humphreys, P. N. Hoffman

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Hardcover | 19 November 1992

At a Glance

Hardcover
320 Pages

Dimensions(cm)
24.3 x 16.3 x 2.3

Hardcover

RRP $431.00

$308.75

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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 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.

Industry Reviews

'The authors give a modern exposition of Schur's results and systematize the recent developments in projective representations of the group Sn.' M. Nazarov, Mathematics Abstracts, 779/94

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