On quantum separation of variables beyond fundamental representations

We describe the extension, beyond fundamental representations of Yang-Baxter algebra, our new construction separation variables bases for quantum integrable lattice models. The key idea underlying approach is to use commuting conserved charges models generate in which their spectral problem separated, i.e. wave functions are factorized terms specific solutions a functional equation. For so-called “non-fundamental” we construct two different types SoV bases. first given from Lax operator having isomorphic auxiliary and spaces that can be obtained by fusion original operator. essentially follows one used previously allows us derive simplicity diagonalizability transfer matrix spectrum. Then, starting using full tower fused matrices, introduce second type proof spectrum naturally derived. show that, under some special choice, this coincides with associated Sklyanin’s approach. Moreover, finite difference (quantum curve) equation set its defining complete This explicitly implemented higher spin general quasi-periodic Y(gl_{2}) Y(gl2) algebra. Our also leads Q display="inline">Q -operator matrices. Finally, family equivalently as enabling