On the Siegel-Weil formula for quaternionic unitary groups

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

我们将西格尔 - 韦伊公式推广到所有四元数对偶对。其应用包括数域上四元数代数上的斜埃尔米特形式的分类问题，以及一个斜埃尔米特形式由另一个斜埃尔米特形式表示的数的加权平均值的乘积公式。