论文标题
分支统一群体的基本变化：严重受损的案件
Base change for ramified unitary groups: the strongly ramified case
论文作者
论文摘要
我们描述了从分支统一组到通用线性组的某些超矛盾表示的基本变化的特殊情况，这些案例都定义在奇数残留特征的P-ADIC领域。粗略地说，我们要求给定超悬式表示的基础层是最大的偏斜，并且该层的田地基准具有最大程度的程度，在基础场上被驯服，并在其子场上被Quadratic撞击，并由定义单位组的Galois参与固定。该超矛盾表示的基本变化是通过其基础简单字符的规范提升，以及其诱导cuspidal类型的级零分量的基础变化，该级别的降低型cuspidal类型的基础变化，该字符由附着在简单字符的内部结构的二次高斯总和上的符号修饰。为了获得此结果，我们研究了抛物线诱导的降低点和仿射Hecke代数上的相应模块，该模块是由覆盖类型定义的，覆盖类型是给定超矛盾表示的类型的乘积和其基本变化的候选者。
We describe a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. Roughly speaking, we require the underlying stratum of a given supercuspidal representation to be skew maximal simple, and the field datum of this stratum to be of maximal degree, tamely ramified over the base field, and quadratic ramified over its subfield fixed by the Galois involution that defines the unitary group. The base change of this supercuspidal representation is described by a canonical lifting of its underlying simple character, together with the base change of the level-zero component of its inducing cuspidal type, modified by a sign attached to a quadratic Gauss sum defined by the internal structure of the simple character. To obtain this result, we study the reducibility points of a parabolic induction and the corresponding module over the affine Hecke algebra, defined by the covering type over the product of types of the given supercuspidal representation and of a candidate of its base change.
