On finite-dimensional representations of one algebra of Temperley-Lieb type (Q2777865)

The author considers finite-dimensional *-representations of the *-algebra generated by projections \(p_1,\dots,p_n\), with the relations \(p_ip_j=0\) if \(|i-j|>1\), \((i,j)\neq(1,n)\); \(p_ip_{i\pm 1}p_i=\tau p_i\), \(p_1p_np_1=\tau p_1\), \(p_np_1p_n=\tau p_n\). The values of \(\tau\in\mathbb{R}\) for which *-representations exist are found. A description of all irreducible *-representations is given.NEWLINENEWLINENEWLINEThe above *-algebra is a modification of the Temperley-Lieb algebra studied by many authors; see e.g. \textit{P. P. Martin} [J. Phys. A 21, No. 3, 577-591 (1988; Zbl 0668.22010)].