BKP and projective Hurwitz numbers

DOI10.1007/s11005-017-0944-0zbMath1368.05009arXiv1501.01283OpenAlexW2963661919MaRDI QIDQ2398260

Alexander Yu. Orlov, Sergey M. Natanzon

Publication date: 15 August 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01283

zbMATH Keywords

hypergeometric functionsrandom matricesprojective planerandom partitionsSchur polynomialsHall-Littlewood polynomialsHurwitz numberstau functionsBKP

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) KdV equations (Korteweg-de Vries equations) (35Q53) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (17)

Fermionic approach to weighted Hurwitz numbers and topological recursion ⋮ BKP and projective Hurwitz numbers ⋮ Weighted Hurwitz numbers and topological recursion: An overview ⋮ From Hurwitz numbers to Feynman diagrams: counting rooted trees in log gravity ⋮ Integrals of tau functions: a round dance tau function and multimatrix integrals ⋮ Character expansion of matrix integrals ⋮ Hurwitz numbers from Feynman diagrams ⋮ BKP hierarchy and Pfaffian point process ⋮ 2D Yang–Mills Theory and Tau Functions ⋮ Weighted Hurwitz numbers and topological recursion ⋮ Hurwitz numbers and products of random matrices ⋮ Notes about the KP/BKP correspondence ⋮ Quantum Hurwitz numbers and Macdonald polynomials ⋮ Non-orientable branched coverings, \(b\)-Hurwitz numbers, and positivity for multiparametric Jack expansions ⋮ Correlation functions of charged free boson and fermion systems ⋮ 2D Toda \(\tau\)-functions as combinatorial generating functions ⋮ On refined Chern-Simons and refined ABJ matrix models

Cites Work

• Unnamed Item
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• On KP-integrable Hurwitz functions
• Simple Hurwitz numbers of a disk
• Complete set of cut-and-join operators in the Hurwitz-Kontsevich theory
• Monotone Hurwitz numbers and the HCIZ integral
• The matrix model for dessins d'enfants
• Matrix models for random partitions
• Solitons and infinite dimensional Lie algebras
• Black holes, \(q\)-deformed 2d Yang--Mills, and non-perturbative topological strings
• Pfaffian and determinantal tau functions
• Multispecies weighted Hurwitz numbers
• Schur function expansion for normal matrix model and associated discrete matrix models
• The KP hierarchy, branched covers, and triangulations
• Noncommutative two-dimensional topological field theories and Hurwitz numbers for real algebraic curves
• Number of nonequivalent coverings over a nonorientable compact surface
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Hypergeometric solutions of soliton equations
• Duality of orthogonal and symplectic matrix integrals and quaternionic Feynman graphs
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• Toda equations for Hurwitz numbers
• Deformed Ginibre ensembles and integrable systems
• The moduli space of curves. Proceedings of the conference held on Texel Island, Netherlands during the last week of April 1994
• Free fermions and tau-functions
• The character of the infinite wedge representation
• Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula
• 2D Toda \(\tau\)-functions as combinatorial generating functions
• A matrix model for hypergeometric Hurwitz numbers
• Hypergeometric \(\tau\)-functions, Hurwitz numbers and enumeration of paths
• Virasoro constraints and topological recursion for Grothendieck's dessin counting
• BKP and projective Hurwitz numbers
• Algebra of differential operators associated with Young diagrams
• Gromov-Witten theory, Hurwitz theory, and completed cycles
• Soliton theory, symmetric functions and matrix integrals
• Intersection theory from duality and replica
• Foundations of the theory of Klein surfaces
• Scalar products of symmetric functions and matrix integrals
• Milne's hypergeometric functions in terms of free fermions
• Matrix Integrals and the Geometry of Spinors
• GENERALIZED KAZAKOV-MIGDAL-KONTSEVICH MODEL: GROUP THEORY ASPECTS
• Monotone Hurwitz Numbers in Genus Zero
• Weighted Hurwitz numbers and hypergeometric $\tau$-functions: an overview
• Integrability of Hurwitz partition functions
• Klein surfaces
• NEW SOLVABLE MATRIX INTEGRALS
• Combinatorial solutions to integrable hierarchies
• Chern–Simons matrix models, two-dimensional Yang–Mills theory and the Sutherland model
• An algebro-geometric proof of Witten’s conjecture
• On Hurwitz numbers and Hodge integrals
• ENUMERATION OF HOMOMORPHISMS AND SURFACE-COVERINGS
• Generating functions for weighted Hurwitz numbers
• Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
• The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
• Transitive factorisations into transpositions and holomorphic mappings on the sphere

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