Symmetric functions, Schubert polynomials, and degeneracy loci:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2001
|
| Schriftenreihe: | SMF/AMS texts and monographs
6 Collection SMF Cours spécialisés ; 3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VII, 167 S. graph. Darst. |
Internformat
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| 240 | 1 | 0 | |a Fonctions symétriques, polynômes de Schubert et lieux de degénérescence |
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| 650 | 4 | |a Schubert, Variétés de | |
| 650 | 7 | |a Symmetrie |2 gtt | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Schubert varieties | |
| 650 | 4 | |a Symmetric functions | |
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Datensatz im Suchindex
| _version_ | 1804129310984896512 |
|---|---|
| adam_text | Titel: Symmetric functions, Schubert polynomials and degeneracy loci
Autor: Manivel, Laurent
Jahr: 2001
Contents
Introduction 1
Chapter 1. The King of Symmetric Functions 7
1.1. Ordinary Functions 7
1.2. Schur Functions 9
1.3. The Kniitli Correspondence 15
1.-1. Some Applications to Symmetric Functions 18
1.5. The Littlewood-Richardson Rule 24
1.0. The Characters of the Symmetric Group 34
1.7. Kostka-Foulkes Polynomials 46
1.8. How the Symmetric Group Acts on Tableaux 52
Chapter 2. Schubert Polynomials 57
2.1. Permutations and the Bruhat Order 57
2.2. Some Classes of Permutations 64
2.3. Schubert Polynomials G9
2.4. Some Properties of Schubert Polynomials 75
2.5. Simple Schubert Polynomials 78
2.6. Flagged Schur Functions 85
2.7. Multiplication of Schur Polynomials 92
2.8. Enumeration of Reduced Words 97
Chapter 3. Schubert Varieties 101
3.1. Grassmannians 101
3.2. Schubert Varieties of Grassmannians 104
3.3. Standard Monomials 111
3.4. Singularities of Schubert Varieties 115
3.5. Characteristic Classes and Degeneracy Loci 121
3.6. Flag Varieties 132
3.7. Singularities of Schubert Varieties, reprise. 142
3.8. Degeneracy Loci and Schubert Polynomials 147
A Brief Introduction to Singular Homology 153
A.l. Singular Homology 153
A.2. Singular Cohoinology 155
A.3. The Fundamental Class and Poincare Duality 156
A.4. Intersection of Algebraic Subvarieties 158
Bibliography 161
Index 165
|
| any_adam_object | 1 |
| author | Manivel, Laurent |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.22 |
| dewey-search | 515/.22 |
| dewey-sort | 3515 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:07Z |
| institution | BVB |
| language | English French |
| lccn | 2001041290 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009882982 |
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| physical | VII, 167 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | SMF/AMS texts and monographs Collection SMF |
| series2 | SMF/AMS texts and monographs Collection SMF : Cours spécialisés |
| spelling | Manivel, Laurent Verfasser aut Fonctions symétriques, polynômes de Schubert et lieux de degénérescence Symmetric functions, Schubert polynomials, and degeneracy loci Laurent Manivel ; translated by John R. Swallow Providence, RI American Mathematical Society 2001 VII, 167 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier SMF/AMS texts and monographs 6 Collection SMF : Cours spécialisés 3 Includes bibliographical references and index Combinatieleer gtt Fonctions symétriques Homologie Polynomen gtt Schubert, Variétés de Symmetrie gtt Homology theory Schubert varieties Symmetric functions Symmetrische Funktion (DE-588)4342453-3 gnd rswk-swf Schubert-Polynom (DE-588)4335881-0 gnd rswk-swf Schubert-Mannigfaltigkeit (DE-588)4512043-2 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Symmetrische Funktion (DE-588)4342453-3 s Schubert-Polynom (DE-588)4335881-0 s Homologietheorie (DE-588)4141714-8 s DE-604 Schubert-Mannigfaltigkeit (DE-588)4512043-2 s 1\p DE-604 SMF/AMS texts and monographs 6 (DE-604)BV013184477 6 Collection SMF Cours spécialisés ; 3 (DE-604)BV012699276 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009882982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Manivel, Laurent Symmetric functions, Schubert polynomials, and degeneracy loci SMF/AMS texts and monographs Collection SMF Combinatieleer gtt Fonctions symétriques Homologie Polynomen gtt Schubert, Variétés de Symmetrie gtt Homology theory Schubert varieties Symmetric functions Symmetrische Funktion (DE-588)4342453-3 gnd Schubert-Polynom (DE-588)4335881-0 gnd Schubert-Mannigfaltigkeit (DE-588)4512043-2 gnd Homologietheorie (DE-588)4141714-8 gnd |
| subject_GND | (DE-588)4342453-3 (DE-588)4335881-0 (DE-588)4512043-2 (DE-588)4141714-8 |
| title | Symmetric functions, Schubert polynomials, and degeneracy loci |
| title_alt | Fonctions symétriques, polynômes de Schubert et lieux de degénérescence |
| title_auth | Symmetric functions, Schubert polynomials, and degeneracy loci |
| title_exact_search | Symmetric functions, Schubert polynomials, and degeneracy loci |
| title_full | Symmetric functions, Schubert polynomials, and degeneracy loci Laurent Manivel ; translated by John R. Swallow |
| title_fullStr | Symmetric functions, Schubert polynomials, and degeneracy loci Laurent Manivel ; translated by John R. Swallow |
| title_full_unstemmed | Symmetric functions, Schubert polynomials, and degeneracy loci Laurent Manivel ; translated by John R. Swallow |
| title_short | Symmetric functions, Schubert polynomials, and degeneracy loci |
| title_sort | symmetric functions schubert polynomials and degeneracy loci |
| topic | Combinatieleer gtt Fonctions symétriques Homologie Polynomen gtt Schubert, Variétés de Symmetrie gtt Homology theory Schubert varieties Symmetric functions Symmetrische Funktion (DE-588)4342453-3 gnd Schubert-Polynom (DE-588)4335881-0 gnd Schubert-Mannigfaltigkeit (DE-588)4512043-2 gnd Homologietheorie (DE-588)4141714-8 gnd |
| topic_facet | Combinatieleer Fonctions symétriques Homologie Polynomen Schubert, Variétés de Symmetrie Homology theory Schubert varieties Symmetric functions Symmetrische Funktion Schubert-Polynom Schubert-Mannigfaltigkeit Homologietheorie |
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