Some finiteness results in the representation theory of isometry groups of regular trees
Küçük Resim Yok
Tarih
2004
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Kluwer Academic Publ
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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.
Açıklama
Anahtar Kelimeler
Category Of Smooth Representations, İsometry Groups Of Regular Trees, Noetherian Categories, Uniform Admissibility
Kaynak
Geometriae Dedicata
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
105
Sayı
1
