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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 050, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.050 (Mi sigma2052) 		 
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential

Gaëtan Borota, Raimar Wulkenhaarb

a Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
b Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
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DOI: https://doi.org/10.3842/SIGMA.2024.050
Abstract: We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan–Plücker relations of certain averages of Schur $Q$-function. The extension of a Pfaffian integration identity of de Bruijn to singular kernels is instrumental in the derivation of the result.
Keywords: BKP hierarchy, matrix models, classical integrability.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 427320536
R.W. was supported by the Cluster of Excellence Mathematics Münster and the CRC 1442 Geometry: Deformations and Rigidity (Funded by the Deutsche Forschungsgemeinschaft Project-ID 427320536 – SFB 1442, as well as under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics Münster: Dynamics – Geometry – Structure).
Received: January 3, 2024; in final form June 1, 2024; Published online June 11, 2024
Document Type: Article
MSC: 37K10, 37K20, 15A15
Language: English
Citation: Gaëtan Borot, Raimar Wulkenhaar, “A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential”, SIGMA, 20 (2024), 050, 16 pp.
Citation in format AMSBIB
\Bibitem{BorWul24}
\by Ga\"etan~Borot, Raimar~Wulkenhaar
\paper A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
\jour SIGMA
\yr 2024
\vol 20
\papernumber 050
\totalpages 16
\mathnet{http://mi.mathnet.ru/sigma2052}
\crossref{https://doi.org/10.3842/SIGMA.2024.050}
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