$gl_{n+1}$ 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

with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of

3 -

body Calogero and Sutherland models are presented.

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