On the deep string spectrum

These proceedings are based on the author's invited talk reviewing the original published work [1,2] of the author with collaborators. The subject matter is a new, covariant and efficient technology of constructing entire trajectories of physical string states deeper inside the string spectrum than the leading Regge. The key observation behind the technology is that the lowering operators of a symplectic algebra appear in the Virasoro constraints which impose physicality of states in the open bosonic string. This algebra commutes with the spacetime Lorentz algebra, (of the little group) of which all string states are irreducible representations. Employing then the so-called Howe duality of representation theory, one may relate the irreducible representations of the two algebras via a bijection. The spectrum thus splits into two parts: trajectories that are lowest weight states of the symplectic algebra and their infinitely many clones. The latter can then be reached by suitably dressing the former with the raising operators of the symplectic algebra. The technology is nontrivially extended to the open superstring, where the relevant Howe dual is an orthosymplectic algebra.