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    An Invitation to Representation Theory: Polynomial Representations of the Symmetric Group

    An Invitation to Representation Theory by Howe, R. Michael;

    Polynomial Representations of the Symmetric Group

    Sorozatcím: Springer Undergraduate Mathematics Series;

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    A termék adatai:

    • Kiadás sorszáma 1st ed. 2022
    • Kiadó Springer
    • Megjelenés dátuma 2022. május 29.
    • Kötetek száma 1 pieces, Book

    • ISBN 9783030980245
    • Kötéstípus Puhakötés
    • Terjedelem229 oldal
    • Méret 235x155 mm
    • Súly 385 g
    • Nyelv angol
    • Illusztrációk XV, 229 p.
    • 516

    Kategóriák

    Rövid leírás:

    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 subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.

    With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.

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    Hosszú leírás:

    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 subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.

    With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.


    ?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)

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    Tartalomjegyzék:

    - 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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