Hypergeometric Solutions of Trigonometric KZ Equations Satisfy Dynamical Difference Equations
Copyright policy )Hypergeometric Solutions of Trigonometric KZ Equations Satisfy Dynamical Difference Equations
Abstract The trigonometric KZ equations associated to a Lie algebra g depend on a parameter λ∈h where h⊂g is a Cartan subalgebra. A system of dynamical difference equations with respect to λ compatible with the KZ equations is introduced by V. Tarasov and the second author (2000, Internat. Math. Res. Notices 15, 801–829). We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to sl N also satisfy the dynamical difference equations.
- University of North Carolina at Chapel Hill United States
Mathematics(all), Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), highest weight module, dynamical difference equation, simple Lie algebra, Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), dynamical equations, trigonometric KZ equation, KZ equations, PBW basis, Discrete version of topics in analysis, hypergeometric solutions, Additive difference equations
Mathematics(all), Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), highest weight module, dynamical difference equation, simple Lie algebra, Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), dynamical equations, trigonometric KZ equation, KZ equations, PBW basis, Discrete version of topics in analysis, hypergeometric solutions, Additive difference equations
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