We compute 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. In this special case, we require the given supercuspidal representation to contain a skew maximal simple stratum, 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.

中文翻译：

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分支单一组的基础更改：强烈分支的情况

我们计算了一个特定的超尖峰表示形式的基础变化的特殊情况，即从一个分支的unit群到一个一般的线性群，两者都在奇数残差特征的ap-adic场上定义。在这种特殊情况下，我们要求给定的超尖峰表示形式包含一个最大的偏斜简单层，并且该层的场数据具有最大程度，在基础场上驯服分枝，并在其伽罗瓦对合确定的子场上二次分枝定义单一组。该超尖峰表示的基本变化通过其基本简单特征的规范提升以及其诱导尖峰类型的零级分量的基本变化来描述，该零变化由附加到内部定义的二次高斯和上的符号修饰简单字符的结构。