Quasi exactly solvable matrix models in sl(n)

TL;DR

This paper extends the construction of quasi exactly solvable matrix models from 2x2 matrices to arbitrary dimension matrices for the algebra sl(n), broadening the scope of solvable models in mathematical physics.

Contribution

It generalizes the previously known 2x2 matrix models for sl(2) to matrices of arbitrary size for sl(n), providing a new framework for quasi exactly solvable models.

Findings

Generalization of sl(2) matrix models to sl(n)

Construction of higher-dimensional quasi exactly solvable models

Potential applications in mathematical physics and representation theory

Abstract

We reconsider the quasi exactly solvable matrix models constructed recently by R. Zhdanov. The 2$\times$2 matrix operators representing the algebra sl(2) are generalized to matrices of arbitrary dimension and a similar construction is achieved for the algebra sl(n).