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Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local equivalence of left-invariant metrics with the same curvature on Lie groups G and G ¯ of dimension three, when G is unimodular and G ¯ is non-unimodular.

Compatibility of the theta correspondence with the Whittaker functors

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

We prove that the global geometric theta-lifting functor for the dual pair ( H , G ) is compatible with the Whittaker functors, where ( H , G ) is one of the pairs ( S 𝕆 2 n , 𝕊 p 2 n ) , ( 𝕊 p 2 n , S 𝕆 2 n + 2 ) or ( 𝔾 L n , 𝔾 L n + 1 ) . That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H .

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