  The Sklyanin algebra admits realizations by difference operators acting on
theta functions. Sklyanin found an invariant metric for the action and
conjectured an explicit formula for the corresponding reproducing kernel. We
prove this conjecture, and also give natural biorthogonal and orthogonal bases
for the representation space. Moreover, we discuss connections with elliptic
hypergeometric series and integrals and with elliptic 6j-symbols.
