  Let $D$ be an irreducible bounded symmetric domain with biholomorphism group
$G$ with maximal compact subgroup $K$. For the Toeplitz operators with
$K$-invariant symbols we provide explicit simultaneous diagonalization formulas
on every weighted Bergman space. The expressions are given in the general case,
but are also worked out explicitly for every irreducible bounded symmetric
domain including the exceptional ones.
