Research ArticleNo Access

On the representation theory of the infinite Temperley–Lieb algebra

Department of Mathematics, Ben Gurion University, Beer-Sheva, Israel

Present address: Mathematics Department, Vrije Universiteit Brussel, Belgium.

https://doi.org/10.1142/S0219498821502054Cited by:1 (Source: Crossref)

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.

Communicated by J. Brundan

Keywords:

AMSC: 20G42, 81R05, 81R10

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