# Title: Braid group, Askey-Wilson algebra and centralizers of U_q(sl_2)

### APA

Zaimi, M. (2023). Title: Braid group, Askey-Wilson algebra and centralizers of U_q(sl_2). Perimeter Institute. https://pirsa.org/23090099

### MLA

Zaimi, Meri. Title: Braid group, Askey-Wilson algebra and centralizers of U_q(sl_2). Perimeter Institute, Sep. 14, 2023, https://pirsa.org/23090099

### BibTex

@misc{ pirsa_PIRSA:23090099, doi = {10.48660/23090099}, url = {https://pirsa.org/23090099}, author = {Zaimi, Meri}, keywords = {Mathematical physics}, language = {en}, title = {Title: Braid group, Askey-Wilson algebra and centralizers of U_q(sl_2)}, publisher = {Perimeter Institute}, year = {2023}, month = {sep}, note = {PIRSA:23090099 see, \url{https://pirsa.org}} }

**Collection**

**Subject**

In this talk, I will consider the centralizer of the quantum group U_q(sl_2) in the tensor product of three identical spin representations. The case of spin 1/2 (fundamental representation) is understood within the framework of the Schur-Weyl duality for U_q(sl_N), and the centralizer is known to be isomorphic to a Temperley-Lieb algebra. The case of spin 1 has also been studied and corresponds to the Birman-Murakami-Wenzl algebra. For a general spin, I will explain how to describe explicitly the centralizer (by generators and relations) using a combination of the braid group algebra and the Askey-Wilson algebra, which has been introduced in the context of orthogonal polynomials.

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Zoom link: https://pitp.zoom.us/j/98471794356?pwd=NjZFdjRFaDFON05HNkdTZS9hZTUvQT09