Jacobi-Trudi Identity in Super Chern-Simons Matrix Model

TL;DR

This paper proves the Jacobi-Trudi identity for the super Chern-Simons matrix model, indicating an underlying integrable structure, building on previous work on the shifted Giambelli identity.

Contribution

It establishes the Jacobi-Trudi identity for the super Chern-Simons matrix model using the shifted Giambelli identity, suggesting integrability.

Findings

Proved the Jacobi-Trudi identity in the super Chern-Simons matrix model.

Connected the identity to an integrable structure of the model.

Extended previous results on the shifted Giambelli identity.

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.