论文标题
全体形态离散系列贡献对广义惠特克式公式的贡献
The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula
论文作者
论文摘要
对于Hermitian Lie组$ g $的管类型，我们找到了Holomorphic离散系列对Whittaker Space的Plancherel分解的贡献，其中$ n $是Siegel Parabolic副群和$ n $ $ n $ n $ nitibecenteral n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。全体形态离散系列嵌入是根据广义的惠特克向量构建的，我们在界面域实现，管域实现和$ l^2 $ - 模型中找到了明确的公式。尽管$ l^2（g/n，ψ）$一般没有有限的多重性，但全体形态离散的系列贡献确实如此。 此外，我们还获得了一个明确的公式，用于全体形态离散系列嵌入的形式维度，并将holomorthic离散系列贡献解释为$ l^2（g/n，ψ）$作为全体形函数的边界值，在域中$ g _ { $ \ MATHCAL {H} _2（ξ，ψ）$。
For a Hermitian Lie group $G$ of tube type we find the contribution of the holomorphic discrete series to the Plancherel decomposition of the Whittaker space $L^2(G/N,ψ)$, where $N$ is the unipotent radical of the Siegel parabolic subgroup and $ψ$ is a certain non-degenerate unitary character on $N$. The holomorphic discrete series embeddings are constructed in terms of generalized Whittaker vectors for which we find explicit formulas in the bounded domain realization, the tube domain realization and the $L^2$-model of the holomorphic discrete series. Although $L^2(G/N,ψ)$ does not have finite multiplicities in general, the holomorphic discrete series contribution does. Moreover, we obtain an explicit formula for the formal dimensions of the holomorphic discrete series embeddings, and we interpret the holomorphic discrete series contribution to $L^2(G/N,ψ)$ as boundary values of holomorphic functions on a domain $Ξ$ in a complexification $G_{\mathbb{C}}$ of $G$ forming a Hardy type space $\mathcal{H}_2(Ξ,ψ)$.
