Abstract :
Let image denote a field, and let V denote a vector space over image of finite positive dimension. An ordered triple A, A*, Adiamond, open of linear operators on V is said to be a Leonard triple whenever for each Bset membership, variant{A,A*,Adiamond, open}, 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*, Adiamond, open is said to be modular whenever for each Bset membership, variant{A,A*,Adiamond, open}, 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.
