Let

$$\begin{aligned} \mathcal {D}_{16}=\left\{ Z\in \mathcal {M}_{1,2}(\mathfrak {C}^{c}):\;\begin{array}{lll} 1-\left\langle Z,Z \right\rangle +\left\langle Z^{\sharp },Z^{\sharp }\right\rangle>0,\\ 2-\left\langle Z,Z \right\rangle \; >0\end{array}\right\} \end{aligned}$$

be an exceptional domain of non-tube type and let \(\mathcal {U}_{\nu }\) and \(\mathcal {W}_{\nu }\) the associated generalized Hua operators. In this paper, we determine the explicit formula of the action of the group \( E_{6(-14)}\) on \(\mathcal {D}_{16}\). We characterized the \(L^{p}\)-range, \(1\le p < \infty \) of the generalized Poisson transform on the Shilov boundary of the domain \(\mathcal {D}_{16}\).

中文翻译：

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异常域的调和分析 $$E_{6(-14)}/U(1)Spin(10)$$

Let

$$\begin{对齐} \mathcal {D}_{16}=\left\{ Z\in \mathcal {M}_{1,2}(\mathfrak {C}^{c}):\;\开始{数组}{lll} 1-\left\langle Z,Z \right\rangle +\left\langle Z^{\sharp },Z^{\sharp }\right\rangle>0,\\ 2-\左\rangle Z,Z \右\rangle \; >0\end{数组}\right\} \end{对齐}$$

是非管类型的特殊域，并设 \(\mathcal {U}_{\nu }\) 和 \(\mathcal {W}_{\nu }\) 关联的广义 Hua 算子。在本文中，我们确定了群 \( E_{6(-14)}\) 对 \(\mathcal {D}_{16}\) 的作用的显式公式。我们在域 \(\mathcal {D}_{16}\) 的 Shilov 边界上表征了广义泊松变换的 \(L^{p}\) 范围，\(1\le p < \infty \) ）。