Skip to Main content Skip to Navigation
Journal articles

Temperley–Lieb, Birman–Murakami–Wenzl and Askey–Wilson Algebras and Other Centralizers of $U_q(\mathfrak {sl}_2)$

Abstract : The centralizer of the image of the diagonal embedding of $U_q(\mathfrak {sl}_2)$ 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.
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02933969
Contributor : Inspire Hep Connect in order to contact the contributor
Submitted on : Tuesday, September 8, 2020 - 11:01:06 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:32 PM

Links full text

Identifiers

Collections

Citation

Nicolas Crampé, Luc Vinet, Meri Zaimi. Temperley–Lieb, Birman–Murakami–Wenzl and Askey–Wilson Algebras and Other Centralizers of $U_q(\mathfrak {sl}_2)$. Annales Henri Poincare, 2021, 22 (10), pp.3499-3528. ⟨10.1007/s00023-021-01064-x⟩. ⟨hal-02933969⟩

Share

Metrics

Record views

44