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The sign of Galois representations attached to automorphic forms for unitary groups
| Content Provider | Scilit |
|---|---|
| Author | Bellaïche, Joël Chenevier, Gaëtan |
| Copyright Year | 2011 |
| Description | Journal: Compositio Mathematica Let K be a CM number field and $G_{K}$ its absolute Galois group. A representation of $G_{K}$ 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 $G_{K}$ 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 $GL_{n}(𝔸_{K}$), 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 $GL_{n}$ $(𝔸_{F}$) when F is a totally real number field. |
| Ending Page | 1352 |
| Starting Page | 1337 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x11005264 |
| Journal | Compositio Mathematica |
| Issue Number | 5 |
| Volume Number | 147 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2011-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics Particles and Fields Physics Automorphic Form Number Theory Representation Theory Galois Representation Unitary Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
