An orthogonal realization of representations of the Temperley-Lieb algebra

Stephen Doty; Anthony Giaquinto

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arXiv · 2306.17352

An orthogonal realization of representations of the Temperley-Lieb algebra

Stephen Doty·Anthony Giaquinto

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Abstract

Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$, where $V=V(1)$ is the simple module of highest weight $1$ for the quantized enveloping algebra $\mathbf{U}(\mathfrak{sl}_2)$. We give a number of applications, one of which is an orthogonal basis of the simple modules for the Temperley-Lieb algebra $\text{TL}_n$. We relate this new orthogonal basis to the standard cellular basis.

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BibTeX RIS

Stephen Doty, Anthony Giaquinto. 2023-12-08. An orthogonal realization of representations of the Temperley-Lieb algebra. https://arxiv.org/abs/2306.17352

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