Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of $U_q(\mathfrak{sl}_2)$
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Publication:6346899
DOI10.1007/S00023-021-01064-XzbMATH Open1522.17019arXiv2008.04905MaRDI QIDQ6346899
Nicolas Crampé, Luc Vinet, Meri Zaimi
Publication date: 10 August 2020
Abstract: The centralizer of the image of the diagonal embedding of in the tensor product of three irreducible representations is examined in a Schur-Weyl duality spirit. The aim is to offer a description in terms of generators and relations. A conjecture in this respect is offered with the centralizers presented as quotients of the Askey-Wilson algebra. Support for the conjecture is provided by an examination of the representations of the quotients. The conjecture is also shown to be true in a number of cases thereby exhibiting in particular the Temperley-Lieb, Birman-Murakami-Wenzl and one-boundary Temperley-Lieb algebras as quotients of the Askey-Wilson algebra.
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantum groups (quantized function algebras) and their representations (20G42) Ring-theoretic aspects of quantum groups (16T20)
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