Giambelli Identity in Super Chern-Simons Matrix Model

TL;DR

This paper proves that the Giambelli identity, a fundamental relation in representation theory, remains valid in the super Chern-Simons matrix model even under deformations of the fractional-brane background.

Contribution

It extends the known Giambelli compatibility to deformed backgrounds in the super Chern-Simons matrix model, demonstrating its robustness.

Findings

Giambelli identity holds in super Chern-Simons matrix model

Identity persists under background deformations

Supports the universality of the Giambelli relation

Abstract

A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. Previously it was shown that the identity persists in taking, for each character, the matrix integration in the super Chern-Simons matrix model in the grand canonical ensemble. We prove here that this Giambelli compatibility still holds in the deformation of the fractional-brane background.