Identities between q-hypergeometric and hypergeometric integrals of different dimensions

الأصل · EN

Given complex numbers m₁,l₁ and nonnegative integers m₂,l₂, such that m₁+m₂=l₁+l₂, for any a,b=0,...,(m₂,l₂) we define an l₂-dimensional Barnes type q-hypergeometric integral Iₐ,b(z,μ;m₁,m₂,l₁,l₂) and an l₂-dimensional hypergeometric integral Jₐ,b(z,μ;m₁,m₂,l₁,l₂). The integrals depend on complex parameters z and μ. We show that Iₐ,b(z,μ;m₁,m₂,l₁,l₂) equals Jₐ,b(eμ,z;l₁,l₂,m₁,m₂) up to an explicit factor, thus establishing an equality of l₂-dimensional q-hypergeometric and m₂-dimensional hypergeometric integrals. The identity is based on the (glₖ,glₙ) duality for the qKZ and dynamical difference equations.