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.
Kazuhiko Aomoto. Masahiko Ito. "On the structure of Jackson integrals of $BC_n$ type and holonomic $q$-difference equations." Proc. Japan Acad. Ser. A Math. Sci. 81 (9) 145 - 150, Nov. 2005. https://doi.org/10.3792/pjaa.81.145