论文标题
$ P $ -ADIC $（\ MATHRM {gl} _ {n+1}，\ Mathrm {gl} _n）$ i的商人分支法
Quotient branching law for $p$-adic $(\mathrm{GL}_{n+1}, \mathrm{GL}_n)$ I: generalized Gan-Gross-Prasad relevant pairs
论文作者
论文摘要
令$ g_n = \ mathrm {gl} _n（f）$为非架构本地字段$ f $的一般线性组。我们在确定\ [\ mathrm {hom} _ {g_n}（π，π'）\ neq 0 \]的何时确定\ [\ mathrm {hom} _ {hom} _ {hom} _ {\ neq 0 \]的必要条件的情况下，并证明了足够的条件。这解决了商分支定律的问题。 我们还证明，可以通过基本上可以正方形的表示的一系列衍生物来构造的伯恩斯坦 - Zelevinsky衍生物的任何简单商。该结果转移到A型A型代数中，对经典Pieri的对称组规则进行了概括。 一个关键的新成分是对伯恩斯坦 - Zelevinsky过滤中层的表征，该层有助于分支定律，这是由多重性一个定理获得的标准表示，这也提供了分支定律的改进。另一个主要的新成分是通过采用某些最高衍生物的一些分支定律的构造和伯恩斯坦 - 泽维尔文斯基衍生品的简单商。
Let $G_n=\mathrm{GL}_n(F)$ be the general linear group over a non-Archimedean local field $F$. We formulate and prove a necessary and sufficient condition on determining when \[ \mathrm{Hom}_{G_n}(π, π') \neq 0 \] for irreducible smooth representations $π$ and $π'$ of $G_{n+1}$ and $G_n$ respectively. This resolves the problem of the quotient branching law. We also prove that any simple quotient of a Bernstein-Zelevinsky derivative of an irreducible representation can be constructed by a sequence of derivatives of essentially square-integrable representations. This result transferred to affine Hecke algebras of type A gives a generalization of the classical Pieri's rule of symmetric groups. One key new ingredient is a characterization of the layer in the Bernstein-Zelevinsky filtration that contributes to the branching law, obtained by the multiplicity one theorem for standard representations, which also gives a refinement of the branching law. Another key new ingredient is constructions of some branching laws and simple quotients of Bernstein-Zelevinsky derivatives by taking certain highest derivatives.
