An explicit formula of the unramified Shintani functions for (GSp4,GL2×GL1GL2)

Let F be a non-archimedean local field of arbitrary characteristic. We shall prove the uniqueness of the unramified Shintani functions for (GSp4(F),(GL2×GL1GL2)(F)) and give an explicit formula of those. Our result is a generalization of the result for the split special orthogonal group SO5 due to Kato-Murase-Sugano.