PIRSA:23090099

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

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

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

          @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}}
          }

Meri Zaimi Université de Montréal

DOI 10.48660/23090099
Collection
Talk Type Scientific Series
Subject

Abstract

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