63,10 €*
Versandkostenfrei per Post / DHL
Lieferzeit 4-7 Werktage
For compact Lie groups, the book covers the Peter¿Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius¿Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
For compact Lie groups, the book covers the Peter¿Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius¿Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include
Automorphic Forms and Representations
(Cambridge University Press 1997) and
Algebraic Geometry
(World Scientific 1998).
New edition extensively revised and updated
Includes new material on random matrix theory, such as the Keating-Snaith formula
Contains material on the use of Sage for Lie group problems
Includes more exercises that provide motivation for the reader
n
,
C
).- 6 Vector Fields.- 7 Left-Invariant Vector Fields.- 8 The Exponential Map.- 9 Tensors and Universal Properties.- 10 The Universal Enveloping Algebra.- 11 Extension of Scalars.- 12 Representations of sl(2,
C
).- 13 The Universal Cover.- 14 The Local Frobenius Theorem.- 15 Tori.- 16 Geodesics and Maximal Tori.- 17 The Weyl Integration Formula.- 18 The Root System.- 19 Examples of Root Systems.- 20 Abstract Weyl Groups.- 21 Highest Weight Vectors.- 22 The Weyl Character Formula.- 23 The Fundamental Group.- Part III: Noncompact Lie Groups.- 24 Complexification.- 25 Coxeter Groups.- 26 The Borel Subgroup.- 27 The Bruhat Decomposition.- 28 Symmetric Spaces.- 29 Relative Root Systems.- 30 Embeddings of Lie Groups.- 31 Spin.- Part IV: Duality and Other Topics.- 32 Mackey Theory.- 33 Characters of GL(
n
,
C
).- 34 Duality between
Sk
and GL(
n
,
C
).- 35 The Jacobi-Trudi Identity.- 36 Schur Polynomials and GL(
n
,
C
).- 37 Schur Polynomials and
Sk
. 38 The Cauchy Identity.- 39 Random Matrix Theory.- 40 Symmetric Group Branching Rules and Tableaux.- 41 Unitary Branching Rules and Tableaux.- 42 Minors of Toeplitz Matrices.- 43 The Involution Model for
Sk
.- 44 Some Symmetric Alegras.- 45 Gelfand Pairs.- 46 Hecke Algebras.- 47 The Philosophy of Cusp Forms.- 48 Cohomology of Grassmannians.- Appendix: Sage.- References.- Index.
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xiii
551 S. 90 s/w Illustr. 551 p. 90 illus. |
| ISBN-13: | 9781493938421 |
| ISBN-10: | 1493938428 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bump, Daniel |
| Auflage: | Softcover reprint of the original 2nd ed. 2013 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Graduate Texts in Mathematics |
| Maße: | 235 x 155 x 31 mm |
| Von/Mit: | Daniel Bump |
| Erscheinungsdatum: | 23.08.2016 |
| Gewicht: | 0,85 kg |
Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include
Automorphic Forms and Representations
(Cambridge University Press 1997) and
Algebraic Geometry
(World Scientific 1998).
New edition extensively revised and updated
Includes new material on random matrix theory, such as the Keating-Snaith formula
Contains material on the use of Sage for Lie group problems
Includes more exercises that provide motivation for the reader
n
,
C
).- 6 Vector Fields.- 7 Left-Invariant Vector Fields.- 8 The Exponential Map.- 9 Tensors and Universal Properties.- 10 The Universal Enveloping Algebra.- 11 Extension of Scalars.- 12 Representations of sl(2,
C
).- 13 The Universal Cover.- 14 The Local Frobenius Theorem.- 15 Tori.- 16 Geodesics and Maximal Tori.- 17 The Weyl Integration Formula.- 18 The Root System.- 19 Examples of Root Systems.- 20 Abstract Weyl Groups.- 21 Highest Weight Vectors.- 22 The Weyl Character Formula.- 23 The Fundamental Group.- Part III: Noncompact Lie Groups.- 24 Complexification.- 25 Coxeter Groups.- 26 The Borel Subgroup.- 27 The Bruhat Decomposition.- 28 Symmetric Spaces.- 29 Relative Root Systems.- 30 Embeddings of Lie Groups.- 31 Spin.- Part IV: Duality and Other Topics.- 32 Mackey Theory.- 33 Characters of GL(
n
,
C
).- 34 Duality between
Sk
and GL(
n
,
C
).- 35 The Jacobi-Trudi Identity.- 36 Schur Polynomials and GL(
n
,
C
).- 37 Schur Polynomials and
Sk
. 38 The Cauchy Identity.- 39 Random Matrix Theory.- 40 Symmetric Group Branching Rules and Tableaux.- 41 Unitary Branching Rules and Tableaux.- 42 Minors of Toeplitz Matrices.- 43 The Involution Model for
Sk
.- 44 Some Symmetric Alegras.- 45 Gelfand Pairs.- 46 Hecke Algebras.- 47 The Philosophy of Cusp Forms.- 48 Cohomology of Grassmannians.- Appendix: Sage.- References.- Index.
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xiii
551 S. 90 s/w Illustr. 551 p. 90 illus. |
| ISBN-13: | 9781493938421 |
| ISBN-10: | 1493938428 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bump, Daniel |
| Auflage: | Softcover reprint of the original 2nd ed. 2013 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Graduate Texts in Mathematics |
| Maße: | 235 x 155 x 31 mm |
| Von/Mit: | Daniel Bump |
| Erscheinungsdatum: | 23.08.2016 |
| Gewicht: | 0,85 kg |
Ähnliche Produkte
Aktuell nicht verfügbar
Aktuell nicht verfügbar
Aktuell nicht verfügbar
Aktuell nicht verfügbar
Lieferzeit 1-2 Werktage
Aktuell nicht verfügbar
Lieferzeit 1-2 Wochen
Lieferzeit 1-2 Wochen
