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.

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**Book Description **Springer-Verlag New York Inc., United States, 1999. Paperback. Condition: New. 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. Seller Inventory # KNV9780387974958

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**Book Description **Springer-Verlag New York Inc., United States, 1999. Paperback. Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. 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. Seller Inventory # LIE9780387974958

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**Book Description **Springer-Verlag New York Inc., United States, 1999. Paperback. Condition: New. 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. Seller Inventory # KNV9780387974958

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**Book Description **Condition: 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'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's Character Formula.-4.1: Statements of the Results.-4.2: Irreducible Representations of$${\mathfrak{S}_d}$$.-4.3: Proof of Frobenius'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'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's Theorem and Lie'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. Seller Inventory # K9780387974958

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