Projective Representations of the Symmetric Groups: Q-Functions and Shifted Tableaux

Hardcover | February 1, 1992

byP. N. Hoffman, J. F. Humphreys

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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 forgraduate 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 bookdevelops 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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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 eleme...

P. N. Hoffman is at University of Waterloo. J. F. Humphreys is at University of Liverpool.

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Format:HardcoverPublished:February 1, 1992Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198535562

ISBN - 13:9780198535560

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Table of Contents

1. Projective representations and representation groups2. Representation groups for the symmetric group3. A construction for groups4. Representations of objects in G5. A construction for negative representations6. The basic representation7. The Q-functions8. The irreducible negative representation of Sn9. Explicit Q-functions10. Reduction, branching and degree formulae11. Construction of the irreducible negative representations12. Combinatorial and skew Q-functions13. The shifted Knuth algorithm14. Deeper insertion, evacuation and the product theoremReferencesCharacter tablesIndices

Editorial 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