Modular Leonard triples

Let K denote a field, and let V denote a vector space over K of finite positive dimension. An ordered triple A, A*, A♢ of linear operators on V is said to be a Leonard triple whenever for each B∈{A,A*,A♢}, there exists a basis of V with respect to which the matrix representing B is diagonal and the matrices representing the other two operators are irreducible tridiagonal. A Leonard triple A, A*, A♢ is said to be modular whenever for each B∈{A,A*,A♢}, there exists an antiautomorphism of End(V) which fixes B and swaps the other two operators. We classify the modular Leonard triples up to isomorphism.