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Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance

M. V. Ioffe·A. I. Neelov
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Abstract

Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation) differential operators. These operators intertwine the matrix Hamiltonians corresponding to irreducible representations of the permutation group $S_N$. In particular cases, this method allows to construct a new class of exactly solvable Dirac-like equations and a new class of matrix models with shape invariance. The connection with approach of multidimensional supersymmetric quantum mechanics is established.

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M. V. Ioffe, A. I. Neelov. 2002-09-13. Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance. https://doi.org/10.1088/0305-4470%2F35%2F35%2F306

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