Displaying similar documents to “Non-archimedean induced representations of compact zerodimensional groups”

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...

Erratum

(1993)

Compositio Mathematica

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Canonical subgroups of H 1 ⋊ S ⁢ L ⁢ 2 , R

Filippo De Mari, Krzysztof Nowak (2002)

Bollettino dell'Unione Matematica Italiana

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We classify, up to conjugation, all subgroups of the semidirect products H 1 ⋊ S ⁢ L ⁢ 2 , R and R 2 ⋊ S ⁢ L ⁢ 2 , R . Our methods can also be applied to all Lie groups that are locally isomorphic to them.