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

Abstract

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

22 pages, 2 figures, Dedicated to Miloslav Havlicek on the occasion of his 75th birthday

References in corpus (1)

• An infinite family of solvable and integrable quantum systems on a plane