An Invitation to Representation Theory
Polynomial Representations of the Symmetric Group
Series: Springer Undergraduate Mathematics Series;
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Product details:
- Edition number 1st ed. 2022
- Publisher Springer
- Date of Publication 29 May 2022
- Number of Volumes 1 pieces, Book
- ISBN 9783030980245
- Binding Paperback
- No. of pages229 pages
- Size 235x155 mm
- Weight 385 g
- Language English
- Illustrations XV, 229 p. 516
Categories
Short description:
An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.
Long description:
An Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.
?The book under review is a nice introduction to the representation theory of the symmetric group. ? The book is well structured and enriched with numerous exercises, many of which are solved or with hints for the solution.? (Enrico Jabara, zbMATH 1514.20002, 2023) More
Table of Contents:
- 1. First Steps. - 2. Polynomials, Subspaces and Subrepresentations. - 3. Intertwining Maps, Complete Reducibility, and Invariant Inner Products. - 4. The Structure of the Symmetric Group. - 5. Sn-Decomposition of Polynomial Spaces for n = 1, 2, 3. - 6. The Group Algebra. - 7. The Irreducible Representations of Sn: Characters. - 8. The Irreducible Representations of Sn: Young Symmetrizers. - 9. Cosets, Restricted and Induced Representations. - 10. Direct Products of Groups, Young Subgroups and Permutation Modules. - 11. Specht Modules. - 12. Decomposition of Young Permutation Modules. - 13. Branching Relations.
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