Zonal polynomials with quaternion matrix arguments are defined and their properties are discussed.The results are crucial in the further study of noncentral distribution of quaternion.

• 把实矩阵变元的带状多项式推广到四元数矩阵变元的情形，给出其相应的一些性质，这些性质在四元数多元统计分析中，已经成为推导非中心分布的必需的工具.