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

ISBN : 9780198535560

P.N. Hoffman; J. F. Humphreys
320 Pages
163 x 243 mm
Pub date
Nov 1992
Oxford Mathematical Monographs
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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 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.


1. Projective representations and representation groups
2. Representation groups for the symmetric group
3. A construction for groups
4. Representations of objects in G
5. A construction for negative representations
6. The basic representation
7. The Q-functions
8. The irreducible negative representation of Sn
9. Explicit Q-functions
10. Reduction, branching and degree formulae
11. Construction of the irreducible negative representations
12. Combinatorial and skew Q-functions
13. The shifted Knuth algorithm
14. Deeper insertion, evacuation and the product theorem
Character tables

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