Functional Analysis and Applications Seminar 

22/06/2009, 10:00 — 16:00 — Room P3.10, Mathematics Building
Pavlo Omel'chenko, Institute of Mathematics, National Academy of Science, Kiev, Ukraine

About *-representations of polynomial semilinear relations

We study *-representations of semilinear relations with polynomial characteristic functions. For any finite simple non-oriented graph $\Gamma$ we construct a polynomial characteristic function such that $\Gamma$ is its graph. A 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 semilinear relation with quadratic characteristic function and condition of $G$-orthoscalarity is not *-wilde. This class of relations contains, in particular, *-representations of \(U_q(so(3))\).