A determinant formula associated with the elliptic hypergeometric integrals of type $B{C}_n$

Abstract

We establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type $B{C}_n$ by studying the structure of $q$-difference equations to be satisfied by them. The determinant formula is proved by combining the $q$-difference equations of the determinant and its asymptotic analysis along the singularities. The elliptic interpolation functions of type $B{C}_n$ are essentially used in the study of the $q$-difference equations.

44 pages. V3: minor corrections

References in corpus (4)

• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Derivation of a $B{C}_n$ elliptic summation formula via the fundamental invariants
• Evaluation of the $B{C}_n$ elliptic Selberg integral via the fundamental invariants
• A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $B{C}_n$

Cited by in corpus (1)

• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators