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arXiv · 1904.12301

On the Representation theory of the Infinite Temperley-Lieb algebra

Stephen T. Moore
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Abstract

We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or indecomposable. We also define a construction of projective indecomposable representations for $TL_{n}$ that generalizes to give extensions of $TL_{\infty}$ representations. Finally we define a generalization of the spin chain representation and conjecture a generalization of Schur-Weyl duality.

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BibTeXRIS

Stephen T. Moore. 2019-04-28. On the Representation theory of the Infinite Temperley-Lieb algebra. https://doi.org/10.1142/s0219498821502054

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