Displaying similar documents to “On Tunnell’s formula for characters of G L ( 2 ) ”

A remark on by Lafforgue

Hervé Jacquet (2012)

Annales de l’institut Fourier

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Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.

Restricting cuspidal representations of the group of automorphisms of a homogeneous tree

Donald I. Cartwright, Gabriella Kuhn (2003)

Bollettino dell'Unione Matematica Italiana

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Let X be a homogeneous tree in which every vertex lies on q + 1 edges, where q ≥ 2 . Let A = A ⁢ u ⁢ t ⁢ X be the group of automorphisms of X , and let H be the its subgroup P ⁢ G ⁢ L ⁢ 2 , F , where F is a local field whose residual field has order q . We consider the restriction to H of a continuous irreducible unitary representation π of A . When π is spherical or special, it was well known that π remains irreducible, but we show that when π is cuspidal, the situation is much more complicated. We then study in detail what happens...