The sign of Galois representations attached to automorphic forms for unitary groups
The sign of Galois representations attached to automorphic forms for unitary groups
复制标题
酉群自守形式上的伽罗瓦表示的符号
DOI：
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发表时间：
2008
影响因子：
1.8
通讯作者：
Gaëtan Chenevier
中科院分区：
文献类型：
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作者：
J. Bellaiche;Gaëtan Chenevier
设K是CM数域，GK是绝对伽罗华群。如果GK的表示同构于它的外复共轭的逆同构，则称它是极化的，直到割圆特征标的幂的扭曲。GK的绝对不可约极化表示的符号为±1，推广了自对偶绝对不可约表示是辛或正交的事实。如果Π是Gln(？k)的正则代数、极化、尖点自同构表示，如果ρ是附着于Π的p-进伽罗瓦表示，则ρ是极化的，并且我们证明了它的所有极化不可约分支都有符号+1。特别地，当F是全实数域时，我们确定了与GLN(？F)的正则代数、本质上自对偶、尖角自同构表示相关的伽罗瓦表示的正交/辛替代。
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.