Finite Chern-Simons matrix model - algebraic approach

TL;DR

This paper explores the algebraic structure of the finite Chern-Simons matrix model, revealing its equivalence to the Calogero model and describing quasiparticle states using Schur functions.

Contribution

It identifies the algebra of observables of the Chern-Simons matrix model with that of the Calogero model and maps their state spaces explicitly.

Findings

Algebra of observables matches between models

States in the models are explicitly identified

Quasiparticle and quasihole states described with Schur functions

Abstract

We analyze the algebra of observables and the physical Fock space of the finite Chern-Simons matrix model. We observe that the minimal algebra of observables acting on that Fock space is identical to that of the Calogero model. Our main result is the identification of the states in the l-th tower of the Chern-Simons matrix model Fock space and the states of the Calogero model with the interaction parameter nu=l+1. We describe quasiparticle and quasihole states in the both models in terms of Schur functions, and discuss some nontrivial consequences of our algebraic approach.