Identities for hypergeometric integrals of different dimensions
Abstract
Given complex numbers m1,l1 and positive integers m2,l2, such that m1+m2=l1+l2, we define l2-dimensional hypergeometric integrals Ia,b(z;m1,m2,l1,l2), a,b=0,...,(m2,l2), depending on a complex parameter z. We show that Ia,b(z;m1,m2,l1,l2)=Ia,b(z;l1,l2,m1,m2), thus establishing an equality of l2 and m2-dimensional integrals. This identity allows us to study asymptotics of the integrals with respect to their dimension in some examples. The identity is based on the (glk,gln) duality for the KZ and dynamical differential equations.
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