# Representation Theory: A First Course (Graduate Texts in Mathematics / Readings in Mathematics)

## Fulton, William; Harris, Joe

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Reseña del editor:

The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

Reseña del editor:

Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

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## 1.Representation Theory

ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
English-Book-Service Mannheim
(Mannheim, Alemania)
Valoración

Descripción Estado de conservación: New. Publisher/Verlag: Springer, Berlin | A First Course | Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups. | The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific. | I: Finite Groups.- 1. Representations of Finite Groups.-1.1: Definitions.-1.2: Complete Reducibility; Schur&apos;s Lemma.-1.3: Examples: Abelian Groups;$${\mathfrak{S}_3}$$.- 2. Characters.-2.1: Characters.-2.2: The First Projection Formula and Its Consequences.-2.3: Examples:$${\mathfrak{S}_4}$$and$${\mathfrak{A}_4}$$.-2.4: More Projection Formulas; More Consequences.- 3. Examples; Induced Representations; Group Algebras; Real Representations.-3.1: Examples:$${\mathfrak{S}_5}$$and$${\mathfrak{A}_5}$$.-3.2: Exterior Powers of the Standard Representation of$${\mathfrak{S}_d}$$.-3.3: Induced Representations.-3.4: The Group Algebra.-3.5: Real Representations and Representations over Subfields of$$\mathbb{C}$$.- 4. Representations of:$${\mathfrak{S}_d}$$Young Diagrams and Frobenius&apos;s Character Formula.-4.1: Statements of the Results.-4.2: Irreducible Representations of$${\mathfrak{S}_d}$$.-4.3: Proof of Frobenius&apos;s Formula.- 5. Representations of$${\mathfrak{A}_d}$$and$$G{L_2}\left( {{\mathbb{F}_q}} \right)$$.-5.1: Representations of$${\mathfrak{A}_d}$$.-5.2: Representations of$$G{L_2}\left( {{\mathbb{F}_q}} \right)$$and$$S{L_2}\left( {{\mathbb{F}_q}} \right)$$.- 6. Weyl&apos;s Construction.-6.1: Schur Functors and Their Characters.-6.2: The Proofs.- II: Lie Groups and Lie Algebras.- 7. Lie Groups.-7.1: Lie Groups: Definitions.-7.2: Examples of Lie Groups.-7.3: Two Constructions.- 8. Lie Algebras and Lie Groups.-8.1: Lie Algebras: Motivation and Definition.-8.2: Examples of Lie Algebras.-8.3: The Exponential Map.- 9. Initial Classification of Lie Algebras.-9.1: Rough Classification of Lie Algebras.-9.2: Engel&apos;s Theorem and Lie&apos;s Theorem.-9.3: Semisimple Lie Algebras.-9.4: Simple Lie Algebras.- 10. Lie Algebras in Dimensions One, Two, and Three.-10.1: Dimensions One and Two.-10.2: Dimension Three, Rank 1.-10.3: Dimension Three, Rank 2.-10.4: Dimension Three, Rank 3.- 11. Representations of$$\mathfrak{s}{\mathfrak{l}_2}\mathbb{C}$$.-11.1: The Irreducible Representations.-11.2: A Little Plethysm.-11.3: A Little Geometric Plethysm.- 12. Representations of$$\mathfrak{s}{\mathfrak{l}_3}\mathbb{C},$$Part I.- 13. Representations of$$\mathfrak{s}{\mathfrak{l}_3}\mathbb{C},$$Part II: Mainly Lots of Examples.-13.1: Examples.-13.2: Description of the Irreducible Representation. Nº de ref. de la librería K9780387974958

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## 2.Representation Theory: A First Course (Paperback)

Editorial: Springer-Verlag New York Inc., United States (1999)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Springer-Verlag New York Inc., United States, 1999. Paperback. Estado de conservación: New. 231 x 155 mm. Language: English . Brand New Book. The primary goal of these lectures is to introduce a beginner to the finite- dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific. 1st Corrected ed. 2004. Corr. 3rd printing 1999. Nº de ref. de la librería KNV9780387974958

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## 3.Representation Theory: A First Course (Paperback)

Editorial: Springer-Verlag New York Inc., United States (1999)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
The Book Depository
(London, Reino Unido)
Valoración

Descripción Springer-Verlag New York Inc., United States, 1999. Paperback. Estado de conservación: New. 231 x 155 mm. Language: English . Brand New Book. The primary goal of these lectures is to introduce a beginner to the finite- dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific. 1st Corrected ed. 2004. Corr. 3rd printing 1999. Nº de ref. de la librería KNV9780387974958

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## 4.Representation Theory

Editorial: Springer Jul 1999 (1999)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Rheinberg-Buch
Valoración

Descripción Springer Jul 1999, 1999. Taschenbuch. Estado de conservación: Neu. 235x155x30 mm. Neuware - The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific. 568 pp. Englisch. Nº de ref. de la librería 9780387974958

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## 5.Representation Theory

Editorial: Springer Jul 1999 (1999)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Agrios-Buch
Valoración

Descripción Springer Jul 1999, 1999. Taschenbuch. Estado de conservación: Neu. 235x155x30 mm. Neuware - The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific. 568 pp. Englisch. Nº de ref. de la librería 9780387974958

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## 6.Representation Theory

Editorial: Springer-Verlag New York Inc. 1991-01-01, New York, NY (1991)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Blackwell's
(Oxford, OX, Reino Unido)
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Descripción Springer-Verlag New York Inc. 1991-01-01, New York, NY, 1991. paperback. Estado de conservación: New. Nº de ref. de la librería 9780387974958

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## 7.Representation Theory

Editorial: Springer-Verlag New York Inc. (1999)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Valoración

Descripción Springer-Verlag New York Inc., 1999. Estado de conservación: New. Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups. Series: Graduate Texts in Mathematics. Num Pages: 566 pages, biography. BIC Classification: PBG; PBKF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 160 x 30. Weight in Grams: 790. . 1999. Corrected. Paperback. . . . . . Nº de ref. de la librería V9780387974958

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## 8.Representation Theory

Editorial: Springer-Verlag New York Inc.
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Kennys Bookstore
(Olney, MD, Estados Unidos de America)
Valoración

Descripción Springer-Verlag New York Inc. Estado de conservación: New. Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups. Series: Graduate Texts in Mathematics. Num Pages: 566 pages, biography. BIC Classification: PBG; PBKF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 160 x 30. Weight in Grams: 790. . 1999. Corrected. Paperback. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780387974958

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## 9.Representation Theory

Editorial: Springer-Verlag New York Inc. (1991)
ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
Books2Anywhere
(Fairford, GLOS, Reino Unido)
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Descripción Springer-Verlag New York Inc., 1991. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería BB-9780387974958

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## 10.Representation Theory: A First Course

ISBN 10: 0387974954 ISBN 13: 9780387974958
Librería
BWB
(Valley Stream, NY, Estados Unidos de America)
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97803879749580000000

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