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Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
Інший ID:
2010 Mathematics Subject Classification: 14H70; 32G34; 14H60
DOI: http://dx.doi.org/10.3842/SIGMA.2012.095
DOI: http://dx.doi.org/10.3842/SIGMA.2012.095
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
509
Завантажень:
232
Анотація:
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.
