PIRSA:24110076 Scientific Series Mathematical physics

DOI10.48660/24110076

Series: Mathematical Physics

Zaimi, M. (2024). Askey-Wilson algebra, Chern-Simons theory and link invariants. Perimeter Institute. https://pirsa.org/24110076

Zaimi, Meri. Askey-Wilson algebra, Chern-Simons theory and link invariants. Perimeter Institute, Nov. 14, 2024, https://pirsa.org/24110076 

@misc{ pirsa_PIRSA:24110076,
  doi = {10.48660/24110076},
  url = {https://pirsa.org/24110076},
  author = {Zaimi, Meri},
  keywords = {Mathematical physics},
  language = {en},
  title = {Askey-Wilson algebra, Chern-Simons theory and link invariants},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {nov},
  note = {PIRSA:24110076 see, \url{https://pirsa.org}}
}

Abstract

Chern-Simons theory is a topological quantum field theory which leads to link invariants, such as the Jones polynomial, through the expectation values of Wilson loops. The same link invariants also appear in a mathematical construction of Reshetikhin and Turaev which uses a trace on Yang-Baxter operators. Several algebraic structures are involved in these frameworks for computing link invariants, including the braid group, quantum algebras and centralizer algebras (such as the Temperley-Lieb algebra). In this talk, I will explain how the Askey-Wilson algebra, originally introduced in the context of orthogonal polynomials, can also be understood within the Chern-Simons theory and the Reshetikhin-Turaev link invariant construction.

Resources

Next talk

Related Talks