Giambelli Identity in Super Chern-Simons Matrix Model

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.

arXiv comment16 pages, 3 figures, v2: introduction extended, references added

References in corpus (29)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Fractional M2-branes
• From weak to strong coupling in ABJM theory
• N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds
• ABJM theory as a Fermi gas
• Non-perturbative effects and the refined topological string
• Exact Results in ABJM Theory from Topological Strings
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• Instanton Bound States in ABJM Theory
• Exact Results on the ABJM Fermi Gas
• ABJ Fractional Brane from ABJM Wilson Loop
• N=4 Chern-Simons theories with auxiliary vector multiplets
• ABJM Wilson Loops in Arbitrary Representations
• 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 Orbifold ABJM Theory
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orientifolding of the ABJ Fermi gas
• Exact results for ABJ Wilson loops and open-closed duality

Cited by in corpus (11)

• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Hanany-Witten Transition in Quantum Curves
• Matrix models for classical groups and Toeplitz$\pm$Hankel minors with applications to Chern-Simons theory and fermionic models
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• 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