4 research outputs found
Multiparticle SUSY quantum mechanics and the representations of permutation group
The method of multidimensional SUSY Quantum Mechanics is applied to the
investigation of supersymmetrical N-particle systems on a line for the case of
separable center-of-mass motion. New decompositions of the superhamiltonian
into block-diagonal form with elementary matrix components are constructed.
Matrices of coefficients of these minimal blocks are shown to coincide with
matrices of irreducible representations of permutations group S_N, which
correspond to the Young tableaux (N-M,1^M). The connections with known
generalizations of N-particle Calogero and Sutherland models are established.Comment: 20 pages, Latex,no figure
Integrable Spin Chain with Reflecting End
A new integrable spin chain of the Haldane-Shastry type is introduced. It is
interpreted as the inverse-square interacting spin chain with a {\it reflecting
end}. The lattice points of this model consist of the square roots of the zeros
of the Laguerre polynomial. Using the ``exchange operator formalism'', the
integrals of motion for the model are explicitly constructed.Comment: 13 pages, REVTeX3, with minor correction
Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
Intertwining relations for -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 . 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.Comment: 24 p.