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Displaying similar documents to “A canonical map between Hecke algebras”

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...

On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

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Let D ( s , f , g ) be the Rankin product L -function for two Hilbert cusp forms f and g . This L -function is in fact the standard L -function of an automorphic representation of the algebraic group G L ( 2 ) × G L ( 2 ) defined over a totally real field. Under the ordinarity assumption at a given prime p for f and g , we shall construct a p -adic analytic function of several variables which interpolates the algebraic part of D ( m , f , g ) for critical integers m , regarding all the ingredients m , f and g as variables.

Relations between jacobians of modular curves of level p 2

Imin Chen, Bart De Smit, Martin Grabitz (2004)

Journal de Théorie des Nombres de Bordeaux

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We derive a relation between induced representations on the group GL 2 ( ℤ / p 2 ℤ ) which implies a relation between the jacobians of certain modular curves of level p 2 . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( ℤ / p 2 ℤ ) .