Nonabelian Fourier transforms for spherical representations
Copyright policy )Nonabelian Fourier transforms for spherical representations
Braverman and Kahzdan have introduced an influential conjecture on local functional equations for general Langlands $L$-functions. It is related to L. Lafforgue's equally influential conjectural construction of kernels for functorial transfers. We formulate and prove a version of Braverman and Kazhdan's conjecture for spherical representations over an archimedean field that is suitable for application to the trace formula. We then give a global application related to Langlands' beyond endoscopy proposal. It is motivated by Ngô's suggestion that one combine nonabelian Fourier transforms with the trace formula in order to prove the functional equations of Langlands $L$-functions in general.
Accepted for publication in the Pacific Journal of Mathematics
- Duke University United States
Representation-theoretic methods; automorphic representations over local and global fields, Mathematics - Number Theory, beyond endoscopy, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, \(L\)-functions, nonabelian Fourier transform, FOS: Mathematics, Number Theory (math.NT), Primary 11F70, Secondary 11F66, 22E45, Representations of Lie and linear algebraic groups over real fields: analytic methods
Representation-theoretic methods; automorphic representations over local and global fields, Mathematics - Number Theory, beyond endoscopy, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, \(L\)-functions, nonabelian Fourier transform, FOS: Mathematics, Number Theory (math.NT), Primary 11F70, Secondary 11F66, 22E45, Representations of Lie and linear algebraic groups over real fields: analytic methods
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