Some Finiteness Results in the Representation Theory of Isometry Groups of Regular Trees
Identifieur interne : 000D91 ( Main/Exploration ); précédent : 000D90; suivant : 000D92Some Finiteness Results in the Representation Theory of Isometry Groups of Regular Trees
Auteurs : Selçuk Demir [Turquie]Source :
- Geometriae Dedicata [ 0046-5755 ] ; 2004-04-01.
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Abstract
Abstract: Let G denote the isometry group of a regular tree of degree ≥3. The notion of congruence subgroup is introduced and finite generation of the congruence Hecke algebras is proven. Let U be congruence subgroup and $$\mathcal{M}$$ (G; U) be the category of smooth representations of G generated by their U-fixed vectors. We also show that this subcategory is closed under taking subquotients. All these results are analogues of well-known results in the case of p-adic groups. It is also shown that the category of admissible representation of G is Noetherian in the sense that every subrepresentation of a finitely generated admissible representation is again finitely generated. Since we want to emphesize the similarities between these groups and p-adic groups, we give the same proofs which also work in the p-adic case whenever possible.
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DOI: 10.1023/B:GEOM.0000024722.31926.97
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