Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously, for the super Chern-Simons matrix model (the spherical one-point function of the superconformal Chern-Simons theory describing the worldvolume of the M2-branes),...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209523 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model / T. Furukawa, S. Moriyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862530735206825984 |
|---|---|
| author | Furukawa, T. Moriyama, S. |
| author_facet | Furukawa, T. Moriyama, S. |
| citation_txt | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model / T. Furukawa, S. Moriyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously, for the super Chern-Simons matrix model (the spherical one-point function of the superconformal Chern-Simons theory describing the worldvolume of the M2-branes), the Giambelli identity was proved from a shifted version of it. With the same shifted Giambelli identity, we can further prove the Jacobi-Trudi identity, which strongly suggests an integrable structure for this matrix model.
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| first_indexed | 2025-12-02T18:53:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209523 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T18:53:31Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Furukawa, T. Moriyama, S. 2025-11-24T10:34:42Z 2018 Jacobi-Trudi Identity in Super Chern-Simons Matrix Model / T. Furukawa, S. Moriyama // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 48 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05E05; 37K10 arXiv: 1711.04893 https://nasplib.isofts.kiev.ua/handle/123456789/209523 https://doi.org/10.3842/SIGMA.2018.049 It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously, for the super Chern-Simons matrix model (the spherical one-point function of the superconformal Chern-Simons theory describing the worldvolume of the M2-branes), the Giambelli identity was proved from a shifted version of it. With the same shifted Giambelli identity, we can further prove the Jacobi-Trudi identity, which strongly suggests an integrable structure for this matrix model. We are especially grateful to Soichi Okada for raising the question discussed in this paper clearly, Yasuhiko Yamada and Sintarou Yanagida for many valuable discussions and instructive comments. We would also like to thank Heng-Yu Chen, Balog Janos, Naotaka Kubo, Satsuki Matsuno, Masatoshi Noumi, Junji Suzuki, Akihiro Tsuchiya, and Marcus Werner for valuable discussions. The work of S.M. is supported by JSPS Grant-in-Aid for Scientific Research (C) #2640024. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Jacobi-Trudi Identity in Super Chern-Simons Matrix Model Article published earlier |
| spellingShingle | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model Furukawa, T. Moriyama, S. |
| title | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model |
| title_full | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model |
| title_fullStr | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model |
| title_full_unstemmed | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model |
| title_short | Jacobi-Trudi Identity in Super Chern-Simons Matrix Model |
| title_sort | jacobi-trudi identity in super chern-simons matrix model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209523 |
| work_keys_str_mv | AT furukawat jacobitrudiidentityinsuperchernsimonsmatrixmodel AT moriyamas jacobitrudiidentityinsuperchernsimonsmatrixmodel |