Differential Equations Compatible with KZ Equations
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We define a system of ‘dynamical’ differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the ‘dual’ variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions.
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- Differential Equations Compatible with KZ Equations
Mathematical Physics, Analysis and Geometry
Volume 3, Issue 2 , pp 139-177
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- Kluwer Academic Publishers
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- hypergeometric solutions
- Kac–Moody Lie algebras
- KZ equations
- Author Affiliations
- 1. Departement Mathematik, ETH-Zentrum, 8092, Zürich, Switzerland
- 2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599 – 3250, U.S.A.
- 3. St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191011, Russia
- 4. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599 – 3250, U.S.A