This article is cited in 9 papers

Jacobi–Trudi Identity in Super Chern–Simons Matrix Model

Tomohiro Furukawa, Sanefumi Moriyama

Department of Physics, Osaka City University, Osaka 558-8585, Japan

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.

Keywords: Jacobi–Trudi identity; ABJM theory; Chern–Simons theory; matrix model; integrable system.

MSC: 05E05; 37K10

Received: January 19, 2018; in final form May 10, 2018; Published online May 18, 2018

Language: English

DOI: 10.3842/SIGMA.2018.049

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