A theta product formula for Jackson integrals associated with root systems
Jackson integrals \(J_R(k,\overline{\xi})\) associated with irreducible reduced root system \(R\) are defined. The formula expressing \(J_R(k,\overline{\xi})\) as the product on \(\alpha \in R^+\) of q-gamma functions and Jacobi elliptic theta functions depending on \(\alpha \) is conjectured. The result according to which this formula is true for \(R\) of type \(A_n, B_2, G_2\) is announced. For these cases the explicit theta product formulas are given.
scientific article; zbMATH DE number 1057079
scientific article