Combinatorics of minuscule representations /:
"Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights m...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
199. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"-- Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups. |
| Beschreibung: | 1 online resource (vii, 320 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107308893 1107308895 9781107314443 1107314445 9781139207003 1139207008 9781299009066 1299009069 9781107306691 1107306698 9781107301603 1107301602 1107236525 9781107236523 1107305764 9781107305762 1107312248 9781107312241 |
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| 245 | 1 | 0 | |a Combinatorics of minuscule representations / |c R.M. Green. |
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| 490 | 1 | |a Cambridge tracts in mathematics ; |v 199 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Introduction -- 1. Classical Lie algebras and Weyl groups -- 2. Heaps over graphs -- 3. Weyl group actions -- 4 Lie theory -- 5. Minuscule representations -- 6. Full heaps over affine Dynkin diagrams -- 7. Chevalley bases -- 8. Combinatorics of Weyl groups -- 9. The 28 bitangents -- 10. Exceptional structures -- 11. Further topics -- Appendix A: Posets, graphs and categories -- Appendix B: Lie theoretic data. | |
| 520 | |a "Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"-- |c Provided by publisher | ||
| 520 | |a Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Representations of Lie algebras. |0 http://id.loc.gov/authorities/subjects/sh2007005290 | |
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| author | Green, R. M., 1971- |
| author_GND | http://id.loc.gov/authorities/names/n2013005374 |
| author_facet | Green, R. M., 1971- |
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| author_sort | Green, R. M., 1971- |
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| contents | Introduction -- 1. Classical Lie algebras and Weyl groups -- 2. Heaps over graphs -- 3. Weyl group actions -- 4 Lie theory -- 5. Minuscule representations -- 6. Full heaps over affine Dynkin diagrams -- 7. Chevalley bases -- 8. Combinatorics of Weyl groups -- 9. The 28 bitangents -- 10. Exceptional structures -- 11. Further topics -- Appendix A: Posets, graphs and categories -- Appendix B: Lie theoretic data. |
| ctrlnum | (OCoLC)827210322 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| genre_facet | Electronic book. |
| id | ZDB-4-EBA-ocn827210322 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:10Z |
| institution | BVB |
| isbn | 9781107308893 1107308895 9781107314443 1107314445 9781139207003 1139207008 9781299009066 1299009069 9781107306691 1107306698 9781107301603 1107301602 1107236525 9781107236523 1107305764 9781107305762 1107312248 9781107312241 |
| language | English |
| oclc_num | 827210322 |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (vii, 320 pages) |
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| publishDate | 2013 |
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| publisher | Cambridge University Press, |
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| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Green, R. M., 1971- https://id.oclc.org/worldcat/entity/E39PCjt8QQJRCWx3wdvdCbqwvd http://id.loc.gov/authorities/names/n2013005374 Combinatorics of minuscule representations / R.M. Green. Cambridge : Cambridge University Press, 2013. 1 online resource (vii, 320 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Cambridge tracts in mathematics ; 199 Includes bibliographical references and index. Introduction -- 1. Classical Lie algebras and Weyl groups -- 2. Heaps over graphs -- 3. Weyl group actions -- 4 Lie theory -- 5. Minuscule representations -- 6. Full heaps over affine Dynkin diagrams -- 7. Chevalley bases -- 8. Combinatorics of Weyl groups -- 9. The 28 bitangents -- 10. Exceptional structures -- 11. Further topics -- Appendix A: Posets, graphs and categories -- Appendix B: Lie theoretic data. "Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"-- Provided by publisher Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups. Print version record. Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Représentations des algèbres de Lie. Analyse combinatoire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Análisis combinatorio embne Lie, Áglebras de embucm Combinatorial analysis fast Representations of Lie algebras fast Electronic book. has work: Combinatorics of minuscule representations (Text) https://id.oclc.org/worldcat/entity/E39PCH7C4wr8cFY9KQPMC9Jfmb https://id.oclc.org/worldcat/ontology/hasWork Print version: Green, R.M., 1971- Combinatorics of minuscule representations. Cambridge : Cambridge University Press, 2013 9781107026247 (DLC) 2012042963 (OCoLC)815364932 Print version: Green, R.M. Combinatorics of Minuscule Representations. Cambridge : Cambridge University Press, ©2013 9781107026247 Cambridge tracts in mathematics ; 199. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=529645 Volltext |
| spellingShingle | Green, R. M., 1971- Combinatorics of minuscule representations / Cambridge tracts in mathematics ; Introduction -- 1. Classical Lie algebras and Weyl groups -- 2. Heaps over graphs -- 3. Weyl group actions -- 4 Lie theory -- 5. Minuscule representations -- 6. Full heaps over affine Dynkin diagrams -- 7. Chevalley bases -- 8. Combinatorics of Weyl groups -- 9. The 28 bitangents -- 10. Exceptional structures -- 11. Further topics -- Appendix A: Posets, graphs and categories -- Appendix B: Lie theoretic data. Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Représentations des algèbres de Lie. Analyse combinatoire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Análisis combinatorio embne Lie, Áglebras de embucm Combinatorial analysis fast Representations of Lie algebras fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2007005290 http://id.loc.gov/authorities/subjects/sh85028802 |
| title | Combinatorics of minuscule representations / |
| title_auth | Combinatorics of minuscule representations / |
| title_exact_search | Combinatorics of minuscule representations / |
| title_full | Combinatorics of minuscule representations / R.M. Green. |
| title_fullStr | Combinatorics of minuscule representations / R.M. Green. |
| title_full_unstemmed | Combinatorics of minuscule representations / R.M. Green. |
| title_short | Combinatorics of minuscule representations / |
| title_sort | combinatorics of minuscule representations |
| topic | Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Représentations des algèbres de Lie. Analyse combinatoire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Análisis combinatorio embne Lie, Áglebras de embucm Combinatorial analysis fast Representations of Lie algebras fast |
| topic_facet | Representations of Lie algebras. Combinatorial analysis. Représentations des algèbres de Lie. Analyse combinatoire. MATHEMATICS Algebra General. MATHEMATICS Algebra Intermediate. Análisis combinatorio Lie, Áglebras de Combinatorial analysis Representations of Lie algebras Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=529645 |
| work_keys_str_mv | AT greenrm combinatoricsofminusculerepresentations |