Mock Tridiagonal Systems

Abstract

We introduce the notion of a {\it mock tridiagonal system}. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain non-vanishing condition. We show how mock tridiagonal systems can be used to construct tridiagonal systems that meet certain specifications. This paper is part of our ongoing project to classify the tridiagonal systems up to isomorphism.

10 pages

References in corpus (9)

• An integrable structure related with tridiagonal algebras
• Deformed Dolan-Grady relations in quantum integrable models
• The structure of quotients of the Onsager algebra by closed ideals
• The Drinfel'd polynomial of a tridiagonal pair
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• The augmented tridiagonal algebra
• Finite-dimensional irreducible modules for the three-point ${\mathfrak{sl}}_2$ loop algebra
• Towards a classification of the tridiagonal pairs
• Tridiagonal pairs of shape (1,2,1)

Cited by in corpus (3)

• A classification of sharp tridiagonal pairs
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• On the shape of a tridiagonal pair