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We provide an explicit expression for the first order $q$-difference systemfor the Jackson integral of symmetric Selberg type. The $q$-difference systemgives a generalization of $q$-analog of contiguous relations for the Gausshypergeometric function. As a basis of the system we use a set of the symmetricpolynomials introduced by Matsuo in his study of the $q$-KZ equation. Our mainresult is an explicit expression for the coefficient matrix of the$q$-difference system in terms of its Gauss matrix decomposition. We introducea class of symmetric polynomials called interpolation polynomials, whichincludes Matsuo's polynomials. By repeated use of three-term relations amongthe interpolation polynomials we compute the coefficient matrix.

$q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type