Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
High Energy Physics - Theory
2018-05-21 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1711.04893,
title = {Jacobi-Trudi Identity in Super Chern-Simons Matrix Model},
author = {Tomohiro Furukawa and Sanefumi Moriyama},
journal= {arXiv preprint arXiv:1711.04893},
year = {2018}
}