Conformal blocks, generalized theta functions and the Verlinde formula:
In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was real...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
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| Schriftenreihe: | New mathematical monographs
42 |
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| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 25 Nov 2021) An introduction to affine lie algebras and the associated groups -- Space of vacua and its propagation -- Factorization theorem for space of vacua -- Fusion ring and explicit verlinde formula -- Moduli stack of quasi-parabolic G-bundles and its uniformization -- Parabolic G-bundles and equivariant G-bundles -- Moduli space of semistable G-bundles over a smooth curve -- Identification of the space of conformal blocks with the space of generalized theta functions -- Picard group of moduli space of G-bundles |
| Beschreibung: | 1 Online-Ressource (xxvii, 509 Seiten) |
| ISBN: | 9781108997003 |
| DOI: | 10.1017/9781108997003 |
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| 520 | |a In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics | ||
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| id | DE-604.BV047655361 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:50:58Z |
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| isbn | 9781108997003 |
| language | English |
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| spelling | Kumar, Shrawan 1953- (DE-588)115543384 aut Conformal blocks, generalized theta functions and the Verlinde formula Shrawan Kumar Cambridge Cambridge University Press 2022 1 Online-Ressource (xxvii, 509 Seiten) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 42 Title from publisher's bibliographic system (viewed on 25 Nov 2021) An introduction to affine lie algebras and the associated groups -- Space of vacua and its propagation -- Factorization theorem for space of vacua -- Fusion ring and explicit verlinde formula -- Moduli stack of quasi-parabolic G-bundles and its uniformization -- Parabolic G-bundles and equivariant G-bundles -- Moduli space of semistable G-bundles over a smooth curve -- Identification of the space of conformal blocks with the space of generalized theta functions -- Picard group of moduli space of G-bundles In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics Lie algebras Moduli theory Fiber bundles (Mathematics) Functions, Theta Conformal invariants Affine algebraic groups Erscheint auch als Druck-Ausgabe 978-1-31-651816-8 https://doi.org/10.1017/9781108997003 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kumar, Shrawan 1953- Conformal blocks, generalized theta functions and the Verlinde formula Lie algebras Moduli theory Fiber bundles (Mathematics) Functions, Theta Conformal invariants Affine algebraic groups |
| title | Conformal blocks, generalized theta functions and the Verlinde formula |
| title_auth | Conformal blocks, generalized theta functions and the Verlinde formula |
| title_exact_search | Conformal blocks, generalized theta functions and the Verlinde formula |
| title_exact_search_txtP | Conformal blocks, generalized theta functions and the Verlinde formula |
| title_full | Conformal blocks, generalized theta functions and the Verlinde formula Shrawan Kumar |
| title_fullStr | Conformal blocks, generalized theta functions and the Verlinde formula Shrawan Kumar |
| title_full_unstemmed | Conformal blocks, generalized theta functions and the Verlinde formula Shrawan Kumar |
| title_short | Conformal blocks, generalized theta functions and the Verlinde formula |
| title_sort | conformal blocks generalized theta functions and the verlinde formula |
| topic | Lie algebras Moduli theory Fiber bundles (Mathematics) Functions, Theta Conformal invariants Affine algebraic groups |
| topic_facet | Lie algebras Moduli theory Fiber bundles (Mathematics) Functions, Theta Conformal invariants Affine algebraic groups |
| url | https://doi.org/10.1017/9781108997003 |
| work_keys_str_mv | AT kumarshrawan conformalblocksgeneralizedthetafunctionsandtheverlindeformula |