منابع مشابه
EXTENSIONS OF REPRESENTATIONS OF p-ADIC GROUPS
We calculate extensions between certain irreducible admissible representations of p-adic groups. To Hiroshi Saito, in memoriam
متن کاملSMOOTH REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS
Smooth representations of p-adic groups arise in number theory mainly through the study of automorphic representations, and thus in the end, for example, from modular forms. We saw in the first lecture by Matt Emerton that a modular form, thought of as function on the set of lattices with level N structure, we obtain a function in C(GL2(Z)\GL2(R) × GL2(Z/N),C) satisfying certain differential eq...
متن کاملREPRESENTATIONS OF CLASSICAL p-ADIC GROUPS
Preface 1 1. Classical groups 4 2. Parabolic induction 10 3. Admissible representations 16 4. Jacquet modules and cuspidal representations 24 5. Composition series of induced representations of SL(2, F ) and GL(2, F ) 34 6. Some examples 39 7. Parabolically induced representations of SL(2, F ) and GL(2, F ) 45 8. Some general consequences 52 9. GL(n, F ) 55 10. GSp(n, F ) 62 11. On the reducibi...
متن کاملEssays on representations of p-adic groups Smooth representations
A smooth G module over R is a representation (π, V ) of G on an R-module V such that each v in V is fixed by an open subgroup of G. A smooth representation (π, V ) is said to be admissible if for each open subgroupK in G the subspace V K of vectors fixed by elements of K is finitely generated overR. UsuallyRwill be a field (necessarily of characteristic 0) in which case this means just that V K...
متن کاملMINI-COURSE: p-MODULAR REPRESENTATIONS OF p-ADIC GROUPS
1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1) continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism ↪−→ irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Current developments in mathematics
سال: 2021
ISSN: ['1089-6384', '2164-4829']
DOI: https://doi.org/10.4310/cdm.2021.v2021.n1.a1