About *-representations of polynomial semilinear relations - Omel'chenko, P. V. (Methods of Functional Analysis and Topology, 2009)
In the present paper we study *-representations of semilinear relations with polynomial characteristic functions. For any finite simple non-oriented graph Γ we construct a polynomial characteristic function such that Γ is its graph. Full description of graphs which satisfy polynomial (degree one and two) semilinear relations is obtained. We introduce the G-orthoscalarity condition and prove that any semili ear relation with quadratic characteristic function and condition of G-orthoscalarity is *-tame. This class of relations contains, in particular, *-representations of U_q(so(3)).