论文标题
全体形态离散系列的广义laguerre函数和惠特克向量
Generalized Laguerre functions and Whittaker vectors for holomorphic discrete series
论文作者
论文摘要
我们在标量型霍明型离散序列表示中及其分析性延续中研究了变性的惠特克载体。在四个不同的实现中，有限的域图片，管域图片，$ l^2 $ - 模型和Fock模型，我们找到了它们的显式$ K $ -Type扩展。该系数是根据相应的对称锥体上的广义laguerre函数表示的，我们将$ k $ type的扩展与公式相关联，用于laguerre多项式的生成函数及其复发关系。
We study degenerate Whittaker vectors in scalar type holomorphic discrete series representations of tube type Hermitian Lie groups and their analytic continuation. In four different realizations, the bounded domain picture, the tube domain picture, the $L^2$-model and the Fock model, we find their explicit $K$-type expansions. The coefficients are expressed in terms of the generalized Laguerre functions on the corresponding symmetric cone, and we relate the $K$-type expansions to the formula for the generating function of the Laguerre polynomials and to their recurrence relations.
