Speaker:  A. Sleptsov (NRC ”Kurchatov Institute”, MIPT, IITP)

Date and time:  29.11.2023, 17:00 (GMT +03:00)

Title: Tug-the-hook symmetry for quantum 6j-symbols

Abstract: Quantum 6j-symbols (Racah-Wigner coefficients) provide isomorphism between two different fusions in tensor product of given three representations of a quntum group. They appear in many contexts: theory of angular momenta in quantum mechanics, calculation of amplitudes in 3d quantum gravity models. In my talk, I will first define the 6j-symbols for the quantum group U_q(sl_N) and review their most important properties: tetrahedral symmetry, the pentagon relation (the Biedenharn-Elliot identity), connections to hypergeometric functions and explicit formulas. Then I’ll talk a little about relations of 6j-symbols with quantum invariants of knots, Turaev-Viro invariants for 3-manifolds, and correlators in (conformal) field theory. Finally, I'll talk about our tug-the-hook conjecture, which suggests the existence of a new large class of symmetries for 6j-symbols.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com