KP integrability through the $$x-y$$ swap relation
Abstract We discuss a universal relation that we call the $$x-y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>-</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:math> swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the $$x-y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>-</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:math> swap relation and KP integrability. As an application, we prove a recent conjecture that relates some particular instances of topological recursion to the Mironov–Morozov–Semenoff matrix integrals.
Authors
- Petr Dunin‐Barkowski (ORCID: https://orcid.org/0000-0003-1475-0534)
- Boris Sergeevich Bychkov (ORCID: https://orcid.org/0000-0002-4441-9343)
- A. Alexandrov (ORCID: https://orcid.org/0000-0002-8464-254X)
- Maxim Eduardovich Kazarian (ORCID: https://orcid.org/0000-0002-3928-8799)
- Sergey Viktorovich Shadrin (ORCID: https://orcid.org/0000-0002-4139-9754)
Institutions
- National Research University Higher School of Economics (RU)
- Skolkovo Institute of Science and Technology (RU)
- Kurchatov Institute (RU)
- Institute for Basic Science (KR)
- Carmel (Israel) (IL)
- University of Amsterdam (NL)
- Moscow Polytechnic University (RU)
- University of Haifa (IL)
Publication Details
- Journal
- Selecta Mathematica
- Published
- 2025-04-01
- DOI
- https://doi.org/10.1007/s00029-025-01035-8
- Citations
- 6
- Primary Topic
- Polynomial and algebraic computation
- Type
- article
- Field-Weighted Citation Impact
- 9.03
Funders
- Israel Science Foundation
- University of Haifa