COMMUTING SQUARES AND INVARIANTS OF COMBI NATORIAL STRUCTURES

We define a notion of Markov commuting square of multimatrix algebras over an arbitrary field. As for von Neumann algebras and subfactors, w e associate to such a square a pair of locally multimatrix algebras. I nvariants of this pair (Weyl group, higher relative commutants) cart b e computed in terms of finite dimensional data. There are many classes of examples provided by classical combinatorial structures such as Ca yley graphs or Hadamard matrices.