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arXiv · 1905.06346

Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2)

Nicolas Crampe·Loïc Poulain d'Andecy·Luc Vinet
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Abstract

In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of su(2). As a first step we show that the Racah algebra always surjects onto the centralizer. We then offer a conjecture regarding the description of the kernel of the map, which depends on the irreducible representations. If true, this conjecture would provide a presentation of the centralizer as a quotient of the Racah algebra. We prove this conjecture in several cases. In particular, while doing so, we explicitly obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary Temperley-Lieb algebra as quotients of the Racah algebra.

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BibTeXRIS

Nicolas Crampe, Loïc Poulain d'Andecy, Luc Vinet. 2019-05-15. Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2). https://arxiv.org/abs/1905.06346

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