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The connection problem associated with a Selberg type integral is solved. The connection coefficients are given in terms of the  q -Racah polynomials. As an application of the explicit expression of the connection coefficients, examples of the monodromy-invariant Hermitian form of non-diagonal type are presented. It is noteworthy that such Hermitian forms are intimately related with the correlation functions of non-diagonal type in   -conformal field theory.

The connection problem associated with a Selberg type integral and the q -Racah polynomials