Abstract:
Model representations are constructed for a system $\{B_k\}_1^n$ of bounded linear selfadjoint operators in
a Hilbert space $H$ such that
\begin{gather*}
[B_k,B_s]=\frac i2\varphi^*R_{k,s}^-\varphi, \qquad
\sigma_k\varphi B_s-\sigma_s\varphi B_k=R_{k,s}^+\varphi,
\\
\sigma_k\varphi\varphi^*\sigma_s-\sigma_s\varphi\varphi^*\sigma_k=2iR_{k,s}^-,
\qquad
1\le k, s\le n,
\end{gather*}
where $\varphi$ is a linear operator from $H$ into a Hilbert space $E$ and
$\{\sigma_k,R_{k,s}^\pm\}_1^n$ are some selfadjoint operators in $E$.
A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for $\{B_k\}_1^n$ is described.
Bibliography: 11 titles.
Keywords:systems of selfadjoint operators, commutation relations, model representations.