$gl_{n+1}$ algebra of Matrix Differential Operators and Matrix Quasi-exactly-solvable Problems

Abstract

The generators of the algebra $gl_{n+1}$ in a form of differential operators of the first order acting on ${\bf R}^n$ with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of $3-$body Calogero and Sutherland models are presented.