A Hurwitz theory avatar of open–closed strings

Abstract

We review and explain an infinite-dimensional counterpart of the Hurwitz theory realization (Alexeevski and Natanzon, Math. Russ. Izv. 72:3–24, 2008) of algebraic open–closed-string model à la Moore and Lazaroiu, where the closed and open sectors are represented by conjugation classes of permutations and the pairs of permutations, i.e. by the algebra of Young diagrams and bipartite graphs, respectively. An intriguing feature of this Hurwitz string model is the coexistence of two different multiplications, reflecting the deep interrelation between the theory of symmetric and linear groups, S ∞ and GL(∞).