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Motivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra Tq. This is an infinite-dimensional associative C-algebra with 1. We classify the finite-dimensional irreducible representations of Tq. All such representations are explicitly constructed via embeddings of Tq into the Uq(sl2)-loop algebra. As an application, tridiagonal...
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= αI +βT, where T is defined by the preceding formula. This matrix arises in many applications, such as n coupled harmonic oscillators and solving the Laplace equation numerically. Clearly M and T have the same eigenvectors and their respective eigenvalues are related by μ = α+βλ . Thus, to understand M it is sufficient to work with the simpler matrix T . Eigenvalues and Eigenvectors of T Usu...
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ژورنال
عنوان ژورنال: Mathematical Modelling of Natural Phenomena
سال: 2014
ISSN: 0973-5348,1760-6101
DOI: 10.1051/mmnp/20149514