ON *-REPRESENTATIONS OF A CLASS OF ALGEBRAS WITH POLYNOMIAL GROWTH RELATED TO COXETER GRAPHS

For a Hilbert space H, we study configurations of its subspaces related to Coxeter graphs G(s1),(s2), s1,s2 is an element of {4, 5}, which are arbitrary trees such that one edge has type si, another one has type s2 and the rest are of type 3. We prove that such irreducible configurations exist only in a finite dimensional H, where the dimension of H does not exceed the number of vertices of the graph by more than twice. We give a description of all irreducible nonequivalent configurations; they are indexed with a continuous parameter. As an example, we study irreducible configurations related to a graph that consists of three vertices and two edges of type s1 and s2.