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.

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Superconformal Chern-Simons Theories from del Pezzo Geometries

Cited by in corpus (6)

• Two-Point Functions in ABJM Matrix Model
• Brane Transitions from Exceptional Groups
• Duality Cascades and Affine Weyl Groups
• Duality Cascades and Parallelotopes
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Quantum Mirror Map for Del Pezzo Geometries