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 |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| 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| _version_ | 1862730607273967616 |
|---|---|
| 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.
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| first_indexed | 2026-03-21T18:14:30Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212257 |
| 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 |
| record_format | dspace |
| 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 published earlier |
| 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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