A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential

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 the Schur -function. The extension of a Pfaffian integ...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2024
Main Authors: Borot, Gaëtan, Wulkenhaar, Raimar
Format: Article
Language:English
Published: Інститут математики НАН України 2024
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212257
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential. Gaëtan Borot and Raimar Wulkenhaar. SIGMA 20 (2024), 050, 16 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Borot, Gaëtan
Wulkenhaar, Raimar
author_facet Borot, Gaëtan
Wulkenhaar, Raimar
citation_txt A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential. Gaëtan Borot and Raimar Wulkenhaar. SIGMA 20 (2024), 050, 16 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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 the Schur -function. The extension of a Pfaffian integration identity of de Bruijn to singular kernels is instrumental in the derivation of the result.
first_indexed 2026-03-21T18:14:30Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-21T18:14:30Z
publishDate 2024
publisher Інститут математики НАН України
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spelling Borot, Gaëtan
Wulkenhaar, Raimar
2026-02-03T07:55:43Z
2024
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential. Gaëtan Borot and Raimar Wulkenhaar. SIGMA 20 (2024), 050, 16 pages
1815-0659
2020 Mathematics Subject Classification: 37K10; 37K20; 15A15
arXiv:2306.01501
https://nasplib.isofts.kiev.ua/handle/123456789/212257
https://doi.org/10.3842/SIGMA.2024.050
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 the Schur -function. The extension of a Pfaffian integration identity of de Bruijn to singular kernels is instrumental in the derivation of the result.
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). Parts of this note were prepared during a workshop at the Erwin Schr¨odinger Institute in Vienna and during a stay at IHES of G.B: we thank these institutions for their hospitality. We thank anonymous referees for valuable comments, which led to the expansion of Sections 3 and 4.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
Article
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spellingShingle A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
Borot, Gaëtan
Wulkenhaar, Raimar
title A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
title_full A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
title_fullStr A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
title_full_unstemmed A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
title_short A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
title_sort note on bkp for the kontsevich matrix model with arbitrary potential
url https://nasplib.isofts.kiev.ua/handle/123456789/212257
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