Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
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| Creator |
Levin, A.M.
Olshanetsky, M.A. Smirnov, A.V. Zotov, A.V. |
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| 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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| Date |
2019-02-18T17:37:32Z
2019-02-18T17:37:32Z 2012 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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