Presented By: Group, Lie and Number Theory Seminar - Department of Mathematics
GLNT: Tetrahedral Symbol and Relative Langlands Duality
Griffin Wang (UM)
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.
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.
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