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Knizhnik-Zamolodchikov-Bernard (KZB) equation on an elliptic curve with amarked point is derived by the classical Hamiltonian reduction and furtherquantization. We consider classical Hamiltonian systems on cotangent bundle tothe loop group $L(GL(N,{\bf C}))$ extended by the shift operators, to berelated to the elliptic module. After the reduction we obtain the Hamiltoniansystem on cotangent bundle to the moduli of holomorphic principle bundles andthe elliptic module. It is a particular example of generalized Hitchin systems(GHS), which are defined as hamiltonian systems on cotangent bundles to themoduli of holomorphic bundles and to the moduli of curves. They are extensionsof the Hitchin systems by the inclusion the moduli of curves. In contrast withthe Hitchin systems the algebra of integrals are noncommutative on GHS. Wediscuss the quantization procedure in our example. The quantization of thequadratic integral leads to the KZB equation. We present the explicite form ofhigher quantum Hitchin integrals, which upon on reducing from GHS phase spaceto the Hitchin phase space gives a particular example of the Belinson-Drinfeldcommutative algebra of differential operators on the moduli of holomorphicbundles.Comment: 11 pages, latex, no figures, Contribution to the Proceedings of the  6th Conference on Mathematical Physics (Moscow, June, 1995

Generalized Hitchin systems and Knizhnik-Zamolodchikov-Bernard equation on elliptic curves