Projective Representations of the Symmetric Groups
Q-Functions and Shifted Tableaux
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher OUP Oxford
- Date of Publication 19 November 1992
- ISBN 9780198535560
- Binding Hardback
- No. of pages320 pages
- Size 243x163x23 mm
- Weight 647 g
- Language English
- Illustrations line figures 0
Categories
Short description:
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.
MoreLong description:
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.
'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
Table of Contents:
Projective representations and representation groups
Representation groups for the symmetric group
A construction for groups
Representations of objects in G
A construction for negative representations
The basic representation
The Q-functions
The irreducible negative representation of Sn
Explicit Q-functions
Reduction, branching and degree formulae
Construction of the irreducible negative representations
Combinatorial and skew Q-functions
The shifted Knuth algorithm
Deeper insertion, evacuation and the product theorem
References
Character tables
Indices
