Communications in Number Theory and Physics

Volume 10 (2016)

Number 1

Local Langlands duality and a duality of conformal field theories

Pages: 1 – 22

DOI: http://dx.doi.org/10.4310/CNTP.2016.v10.n1.a1

Author

Martin T. Luu (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il, U.S.A.)

Abstract

We show that the numerical local Langlands duality for $\mathrm{GL}_n$ and the $\mathrm{T}$-duality of two-dimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its $\ell$-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.

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