Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Σg,n of genus g with n marked points. The bundles are defined by their characteristic classes - elements...
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Інститут математики НАН України
2012
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Zitieren: | Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles / A.M. Levin, M.A. Olshanetsky, A.V. Smirnov, A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 74 назв. — англ. |
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irk-123456789-1486572019-02-19T01:27:59Z Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Σg,n of genus g with n marked points. The bundles are defined by their characteristic classes - elements of H²(Σg,n,Z(G)), where Z(G) is a center of the simple complex Lie group G. The KZB equations are the horizontality condition for the projectively flat connection (the KZB connection) defined on the bundle of conformal blocks over the moduli space of curves. The space of conformal blocks has been known to be decomposed into a few sectors corresponding to the characteristic classes of the underlying bundles. The KZB connection preserves these sectors. In this paper we construct the connection explicitly for elliptic curves with marked points and prove its flatness. 2012 Article Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles / A.M. Levin, M.A. Olshanetsky, A.V. Smirnov, A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 74 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H70; 32G34; 14H60 DOI: http://dx.doi.org/10.3842/SIGMA.2012.095 http://dspace.nbuv.gov.ua/handle/123456789/148657 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Σg,n of genus g with n marked points. The bundles are defined by their characteristic classes - elements of H²(Σg,n,Z(G)), where Z(G) is a center of the simple complex Lie group G. The KZB equations are the horizontality condition for the projectively flat connection (the KZB connection) defined on the bundle of conformal blocks over the moduli space of curves. The space of conformal blocks has been known to be decomposed into a few sectors corresponding to the characteristic classes of the underlying bundles. The KZB connection preserves these sectors. In this paper we construct the connection explicitly for elliptic curves with marked points and prove its flatness. |
| format |
Article |
| author |
Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. |
| spellingShingle |
Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. |
| author_sort |
Levin, A.M. |
| title |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles |
| title_short |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles |
| title_full |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles |
| title_fullStr |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles |
| title_full_unstemmed |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles |
| title_sort |
hecke transformations of conformal blocks in wzw theory. i. kzb equations for non-trivial bundles |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148657 |
| citation_txt |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles / A.M. Levin, M.A. Olshanetsky, A.V. Smirnov, A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 74 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-12T19:54:46Z |
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2025-07-12T19:54:46Z |
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