A Hurwitz theory avatar of open-closed strings

Abstract

We review and explain an infinite-dimensional counterpart of the Hurwitz theory realization of algebraic open-closed string model a la Moore and Lizaroiu, 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 graphes respectively. An intriguing feature of this Hurwitz string model is coexistence of two different multiplications, reflecting the deep interrelation between the theory of symmetric and linear groups S_\infty and GL(\infty).

11 pages

References in corpus (4)

• Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
• On the structure of open-closed topological field theory in two dimensions
• Algebra of differential operators associated with Young diagrams
• Some Comments on Branes, G-flux, and K-theory

Cited by in corpus (6)

• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Permutation Centralizer Algebras and Multi-Matrix Invariants
• Cut-and-join structure and integrability for spin Hurwitz numbers
• Hurwitz numbers from Feynman diagrams
• Asymptotic Hurwitz numbers