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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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Інститут математики НАН України
2012
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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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862573867894046720 |
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| author | Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. |
| author_facet | Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| id | nasplib_isofts_kiev_ua-123456789-148657 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T08:28:04Z |
| publishDate | 2012 |
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| spelling | Levin, A.M. Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. 2019-02-18T17:37:32Z 2019-02-18T17:37:32Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148657 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. The authors are grateful to A. Beilinson, L. Feh´er, B. Feigin, A. Gorsky, S. Khoroshkin, A. Losev, A. Mironov, V. Poberezhny, A. Rosly and A. Stoyanovsky for useful discussions and remarks. The work was supported by grants RFBR-09-02-00393, RFBR-09-01-92437-KEa and by the Federal Agency for Science and Innovations of Russian Federation under contract 14.740.11.0347. The work of A.Z. and A.S. was also supported by the Russian President fund MK-1646.2011.1, RFBR-09-01-93106-NCNILa, RFBR-12-01-00482 and RFBR-12-01-33071 mol a ved. The work of A.L. was partially supported by AG Laboratory GU-HSE, RF government grant, ag. 1111.G34.31.0023. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles Article published earlier |
| spellingShingle | 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. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148657 |
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