Some finiteness results in the representation theory of isometry groups of regular trees

DEMİR S.

GEOMETRIAE DEDICATA, cilt.105, sa.1, ss.189-207, 2004 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 105 Sayı: 1
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1023/b:geom.0000024722.31926.97
  • Dergi Adı: GEOMETRIAE DEDICATA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.189-207
  • Anahtar Kelimeler: category of smooth representations, isometry groups of regular trees, Noetherian categories, uniform admissibility
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

Let G denote the isometry group of a regular tree of degree greater than or equal to3. The notion of congruence subgroup is introduced and finite generation of the congruence Hecke algebras is proven. Let U be congruence subgroup and 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.