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An invitation to representation theory : polynomial representations of the symmetric group
Howe, R. Michael.
- ISBN:9783030980252
- ISBN:9783030980245
- Call Number : QA 171 .H69 2022
- Main Entry: Howe, R. Michael.
- Title:An invitation to representation theory : polynomial representations of the symmetric group [electronic resource] / R. Michael Howe.
- Publisher:Cham : Springer, 2022.
- Physical Description:xv, 229 p.: ill.; 25 cm
- Series:SUMS readings, 2730-5821
- Notes:Includes index
- Subject:Representations of groups.
- Preface
- Introduction
- 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
- 9.1 Restriction
- 9.2 Quotient Spaces
- 9.3 Cosets
- 9.4 Coset Representations of a Group
- 9.5 Induced Representations: Version One
- 9.6 Matrix Realizations and Characters of Induced Representations
- 9.7 Construction of Induced Representations
- 9.8 Frobenius Reciprocity
- 9.9 Induced Representations: Version Two
- 9.10 Hints and Additional Comments
- 10 Direct Products of Groups, Young Subgroups and Permutation Modules
- 11 Specht Modules
- 12 Decomposition of Young Permutation Modules
- 13 Branching Relations
- Bibliography
- Index