G（Q_p）的常表示与基本代数表示
Ordinary representations of G(Q_p) and fundamental algebraic representations
摘要：
设G是Q_p上的可裂连通约化代数群，使得G及其对偶群G-hat都有连通中心.受G（Q_p）的一个假设的p进Langlands对应的启发，我们将G（Q_p）的一个n维普通（即Borel值）表示rho：Gal（Q_p-bar/Q_p）与G-hat（E）联系起来，G（Q_p）在E上的一个酉巴拿赫空间表示Pi（rho）^ord由主列表示构成。(Here，E是Q_p的有限扩张。）我们的构造受到G的所有基本代数表示的张量积的“普通部分”的启发。在F_p的一个有限扩张上也有类似的构造，在后一种情况下，当G=GL_n时，我们在适当的假设下证明了Pi（ρ）阶出现在紧酉群的上同调的ρ-部分中.我们还证明了这个结果在p-adic情况下的一个较弱的版本。
英文摘要：
Let G be a split connected reductive algebraic group over Q_p such that both G and its dual group G-hat have connected centres. Motivated by a hypothetical p-adic Langlands correspondence for G(Q_p) we associate to an n-dimensional ordinary (i.e. Borel valued) representation rho : Gal(Q_p-bar/Q_p) to G-hat(E) a unitary Banach space representation Pi(rho)^ord of G(Q_p) over E that is built out of principal series representations. (Here, E is a finite extension of Q_p.) Our construction is inspired by the "ordinary part" of the tensor product of all fundamental algebraic representations of G. There is an analogous construction over a finite extension of F_p. In the latter case, when G=GL_n we show under suitable hypotheses that Pi(rho)^ord occurs in the rho-part of the cohomology of a compact unitary group. We also prove a weaker version of this result in the p-adic case.
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