We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The sign of Galois representations attached to automorphic forms for unitary groups.
- Authors
Bellaïche, Joël; Chenevier, Gaëtan
- Abstract
Let K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a twist by a power of the cyclotomic character. Absolutely irreducible polarized representations of GK have a sign ±1, generalizing the fact that a self-dual absolutely irreducible representation is either symplectic or orthogonal. If Π is a regular algebraic, polarized, cuspidal automorphic representation of GLn(K), and if ρ is a p-adic Galois representation attached to Π, then ρ is polarized and we show that all of its polarized irreducible constituents have sign +1 . In particular, we determine the orthogonal/symplectic alternative for the Galois representations associated to the regular algebraic, essentially self-dual, cuspidal automorphic representations of GLn (F) when F is a totally real number field.
- Subjects
GALOIS theory; AUTOMORPHISMS; REPRESENTATIONS of algebras; UNITARY groups; EIGENVALUES; MATHEMATICAL forms; ALGEBRAIC varieties
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1337
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005264