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.