Ladder relations for a class of matrix valued orthogonal polynomials Articles uri icon

publication date

  • February 2021

start page

  • 463

end page

  • 497

issue

  • 2

volume

  • 146

International Standard Serial Number (ISSN)

  • 0022-2526

abstract

  • Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on R, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form W(x)=e-nu(x) exAexA* on the real line, where nu is a scalar polynomial of even degree with positive leading coefficient and Alpha is a constant matrix.

keywords

  • integrable systems; ladder relations; mathematical physics; non-abelian toda lattice; orthogonal polynomials