Let F be a CM field with totally real subfield \(F^+\) and let \(\pi \) be a C-algebraic cuspidal automorphic representation of the unitary group \({{\,\mathrm{U}\,}}(a,b)(\mathbf {A}_{F^+})\), whose archimedean components are discrete series or non-degenerate limit of discrete series representations. We attach to \(\pi \) a Galois representation \(R_\pi :{{\,\mathrm{Gal}\,}}(\overline{F}/{F}^+)\rightarrow {}^C{{\,\mathrm{U}\,}}(a,b)(\overline{\mathbf {Q}}_\ell )\) such that, for any complex conjugation element c, \(R_\pi (c)\) is as predicted by the Buzzard–Gee conjecture (Buzzard and Gee, in: Automorphic forms and Galois representa, Cambridge University Press, Cambridge, 2014). As a corollary, we deduce that the Galois representations attached to certain irregular, C-algebraic essentially conjugate self-dual cuspidal automorphic representations of \({{\,\mathrm{GL}\,}}_n(\mathbf {A}_F)\) are odd in the sense of Bellaïche–Chenevier (Compos Math 147(5):1337–1352, 2011).

让˚F是CM字段和完全真实子场\（F ^ + \） ，并让\（\ PI \）是Ç -algebraic尖点酉群的自守表示\（{{\，\ mathrm【U} \， }}（a，b）（\ mathbf {A} _ {F ^ +}）\），其阿基米德成分是离散级数或离散级数表示的非简并极限。我们将\\（\ pi \）附加到Galois表示\（R_ \ pi：{{\，\ mathrm {Gal} \，}}（\ overline {F} / {F} ^ +）\ rightarrow {} ^ C {{\，\ mathrm {U} \，}}（a，b）（\ overline {\ mathbf {Q}} _ \ ell} \）这样，对于任何复杂的共轭元素c，\（R_ \ pi（ C）\）正如Buzzard-Gee猜想所预测的那样（Buzzard和Gee，自：自守形态和伽罗瓦表示法，剑桥大学出版社，剑桥，2014年）。作为推论，我们推论Galois表示与某些不规则C代数本质上共轭\（{{\，\ mathrm {GL} \，}} _ n（\ mathbf {A} _F ）\）是奇数在Bellaïche-Chenevier（Compos数学147（5）的意义上：1337年至1352年，2011年）。