{"product_id":"an-invitation-to-representation-theory-polynomial-representations-of-the-symmetric-group-9783030980245","title":"An Invitation to Representation Theory: Polynomial Representations of the Symmetric Group","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAn Invitation to Representation Theory \u003c\/i\u003eoffers 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.\u003cbr\u003eThe 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.\u003cbr\u003eWith 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“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)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e    Preface\u003cp\u003e\u003c\/p\u003e\u003cp\u003e            Introduction\u003c\/p\u003e\u003cp\u003e            Chapter 1.   First Steps\u003c\/p\u003e\u003cp\u003e            Chapter 2.  Polynomials, Subspaces, and Subrepresentations\u003c\/p\u003e\u003cp\u003e            Chapter 3.  Intertwining Maps, Complete Reducibility, and Invariant Inner Products\u003c\/p\u003e            Chapter 4.  The Structure of the Symmetric Group\u003cp\u003e\u003c\/p\u003e\u003cp\u003e            Chapter 5.  Sn Decomposition of Polynomial Spaces for n= 1,2,3.\u003c\/p\u003e\u003cp\u003e            Chapter 6.  The Group Algebra\u003c\/p\u003e\u003cp\u003e            Chapter 7.  The Irreducible Representations of Sn: Characters\u003c\/p\u003e\u003cp\u003e            Chapter 8.  The Irreducible Representations of Sn: Young Symmetrizers\u003c\/p\u003e\u003cp\u003e            Chapter 9.  Cosets, Restricted and Induced Representations\u003c\/p\u003e\u003cp\u003e            Chapter 10.  Direct Products of Groups, Young Subgroups and Permutation Modules\u003c\/p\u003e\u003cp\u003e            Chapter 11.  Specht Modules\u003c\/p\u003e\u003cp\u003e            Chapter 12.  Decomposition of Young Permutation Modules\u003c\/p\u003e\u003cp\u003e            Chapter 13.  Branching Relations\u003c\/p\u003e\u003cp\u003e            Bibliography \u003c\/p\u003e\u003cp\u003e            Index \u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":52085980758359,"sku":"9783030980245","price":22.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030980245.jpg?v=1762211555","url":"https:\/\/bookcurl.com\/products\/an-invitation-to-representation-theory-polynomial-representations-of-the-symmetric-group-9783030980245","provider":"Book Curl","version":"1.0","type":"link"}