Jacobi-Trudi Identity in Super Chern-Simons Matrix Model

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.