论文标题
Bernstein-Zelevinsky衍生物对自动形式的类似物的类似物
An Analogue of Bernstein-Zelevinsky Derivatives to Automorphic Forms
论文作者
论文摘要
在本文中，引入了$ GL_N（\ Mathbb {a}）$上的自动形式表示的伯恩斯坦 - Zelevinsky衍生物的结构。稍后，我们将考虑诱导的表示\ [I（τ_1，τ_2; \ usewissline {s}）= \ Mathrm {ind} _ {p _ {p _ {[n_1，n_1，n_2]}}}}^{g_n}（Δ Δ（τ_2，n_2）| \ cdot |^{s_2}）。\ \]来自$ gl_n（\ m athbb {a}）$的离散频谱表示，并应用我们的方法研究来自Eisenstein系列的退化惠泰克系列的Eisenstein系列，来自Eisenstein系列的eisenstein系列，该系列是从此类代表和其残留物以及其残留物以及其残基的构建的。该方法可用于根据D. Ginzburg，Y。Cai和B. Liu证明的这种类型的自动形式的惠特克的支持。该方法还将产生有关某些退化惠特克系数的欧拉尔利亚性的新结果。
In this paper, a construction to imitate the Bernstein-Zelevinsky derivative for automorphic representations on $GL_n(\mathbb{A})$ is introduced. We will later consider the induced representation \[I(τ_1,τ_2;\underline{s}) = \mathrm{Ind}_{P_{[n_1,n_2]}}^{G_n}(Δ(τ_1,n_1)|\cdot|^{s_1}\boxtimes Δ(τ_2,n_2)|\cdot|^{s_2}).\] from the discrete spectrum representations of $GL_n(\mathbb{A})$, and apply our method to study the degenerate Whittaker coefficients of the Eisenstein series constructed from such a representation as well as of its residues. This method can be used to reprove the results on the Whittaker support of automorphic forms of such kind proven by D. Ginzburg, Y. Cai and B. Liu. This method will also yield new results on the Eulerianity of certain degenerate Whittaker coefficients.
