On the structure of Jackson integrals of $BC_n$ type and holonomic $q$-difference equations

Abstract

Finiteness of non-symmetric and symmetric cohomologies associated with Jackson integrals of type $BC_n$ is studied. Explicit bases of the cohomologies are also stated. It is shown that the integrals using these bases satisfy holonomic systems of linear $q$-difference equations with respect to the parameters.