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We establish a determinant formula for the bilinear form associated with theelliptic hypergeometric integrals of type $BC_n$ by studying the structure of$q$-difference equations to be satisfied by them. The determinant formula isproved by combining the $q$-difference equations of the determinant and itsasymptotic analysis along the singularities. The elliptic interpolationfunctions of type $BC_n$ are essentially used in the study of the$q$-difference equations.

A determinant formula associated with the elliptic hypergeometric integrals of type $BC_n$