Some Finiteness Results in the Representation Theory of Isometry Groups of Regular Trees |
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Authors: | Selçuk Demir |
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Institution: | (1) Istanbul Bilgi University, Istanbul, Turkey |
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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
(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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Keywords: | category of smooth representations isometry groups of regular trees Noetherian categories uniform admissibility |
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