A class of parameter-dependent commuting matrices
B Sriram Shastry · Journal of Physics A Mathematical and General · 2005
We present a novel class of real symmetric matrices in arbitrary dimension d , linearly dependent on a parameter x . The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all x , and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom. This class of matrices generically violates the Wigner von Neumann non-crossing rule, and is argued to be intimately connected with finite-dimensional Hamiltonians of quantum integrable systems.