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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Authors: Furukawa, T., Moriyama, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209523
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209523
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
spellingShingle Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
Furukawa, T.
Moriyama, S.
title_short 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_sort jacobi-trudi identity in super chern-simons matrix model
author Furukawa, T.
Moriyama, S.
author_facet Furukawa, T.
Moriyama, S.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209523
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.
work_keys_str_mv AT furukawat jacobitrudiidentityinsuperchernsimonsmatrixmodel
AT moriyamas jacobitrudiidentityinsuperchernsimonsmatrixmodel
first_indexed 2025-12-02T18:53:31Z
last_indexed 2025-12-02T18:53:31Z
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