Speaker: Griffin Wang (IAS)

Title: Tetrahedral Symbol and Relative Langlands Duality

Abstract: In the quantum theory of angular momentum, the Racah--Wigner coefficient, often known as the 6-j symbol, is a numerical invariant assigned to a tetrahedron with half-integer edge-lengths. The 6 edge-lengths may be viewed as representations of SU(2) satisfying certain multiplicity-one conditions. One important property of the 6j symbol is its hidden symmetry outside the tetrahedral ones, originally discovered by Regge.

In this talk, we explore a generalized construction, dubbed tetrahedral symbol, in the context of rank-1 semisimple groups over local fields, and explain how the extra symmetries may be explained by relative Langlands duality. Joint work with Akshay Venkatesh.