Mathematical Physics, Analysis and Geometry

, Volume 3, Issue 2, pp 139–177

Differential Equations Compatible with KZ Equations

  • G. Felder
  • Y. Markov
  • V. Tarasov
  • A. Varchenko

DOI: 10.1023/A:1009862302234

Cite this article as:
Felder, G., Markov, Y., Tarasov, V. et al. Mathematical Physics, Analysis and Geometry (2000) 3: 139. doi:10.1023/A:1009862302234


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 zi 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.

hypergeometric solutions Kac–Moody Lie algebras KZ equations 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • G. Felder
    • 1
  • Y. Markov
    • 2
  • V. Tarasov
    • 3
  • A. Varchenko
    • 4
  1. 1.Departement MathematikETH-ZentrumZürichSwitzerland
  2. 2.Department of MathematicsUniversity of North CarolinaChapel HillU.S.A.
  3. 3.St. Petersburg Branch of Steklov Mathematical InstituteSt. PetersburgRussia
  4. 4.Department of MathematicsUniversity of North CarolinaChapel HillU.S.A

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