Projective representations of the symmetric groups : Q-functions and shifted tableaux
著者
書誌事項
Projective representations of the symmetric groups : Q-functions and shifted tableaux
（Oxford mathematical monographs）（Oxford science publications）
Clarendon Press , Oxford University Press, 1992
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注記
Bibliography: p. 282-288
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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
- References
- Character tables
- Indices
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