On *-representations of a class of algebras with polynomial growth related to Coxeter graphs - Strelets, A. V.; Popova, N. D. (Methods of Functional Analysis and Topology, 2011)
For a Hilbert space H, we study configurations of its subspaces related to Coxeter graphs G_s_1,s_2, s_1,s_2{4,5}, which are arbitrary trees such that one edge has type s_1, another one has type s_2 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 s_1 and s_2.