Intersection Cardinality Matrices (ICMs) have rows and columns indexed by the family N(K) of k element subsets of an n element set U, with entries which are functions only of the cardinality of the intersection of the sets marking the row and column. The gravitational forces operating on equal masses in certain configurations can be represented by ICMs. Since N(k) is invariant under the group Sn of permutations of U, the vector space CN over the complex numbers C having as basis the elements of N = N(k) is a module over the group algebra C Sn . The latter can be deformed to a Hecke algebra, which in turn induces a deformation of the gravitational forces of masses in these configurations.