On a theta product formula for Jackson integrals associated with root systems of rank two
The classical Selberg integral, which appears in the random matrix theory, possesses the symmetry with respect to a group \(S_n\) and can be expressed as the product of gamma functions. Analogous integrals, associated with root systems are also expressed in the same way. The present paper is devoted to the study of \(q\)-analogues of Selberg integrals associated with root systems which are called the Jackson integrals of Selberg type. The author conjectures the formula for calculating these integrals as the product of \(q\)-gamma functions and Jacobi elliptic theta functions (the theta product formula). This formula is proved for root systems of rank two.
scientific article; zbMATH DE number 1115527
scientific article