2018/12/29 by Andrey V. Sokolov, А. В. Соколов, Sokolov, Andrey V.
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1812.11274
arxiv created 2018/12/29 · arxiv updated 2019/01/01
In this paper we continue studying of matrix n× n linear differential intertwining operators. The problems of minimization and of reducibility of matrix intertwining operators are considered and criterions of weak minimizability and of regular reducibility are proven. It is shown that in contrast to the scalar case n=1 there are for any n\geqslant2 regularly absolutely irreducible matrix intertwining operators of any order N\geqslant2, \it i.e. operators which cannot be factorized into a product of a matrix intertwining operators of lower orders even with a pole singularity(-ies) into coefficients. The theorem is proven on existence for any matrix intertwining operator QN- of the order N a matrix differential operator QN'+ of other, in general, order N' that intertwines the same Hamiltonians H+ and H- as QN- in the opposite direction and such that the products QN'+QN- and QN-QN'+ are identical polynomials of H+ and H- respectively. Polynomial algebra of supersymmetry corresponding to this case is constructed.