论文标题
一般线性组的Shalika模型
Shalika models for general linear groups
论文作者
论文摘要
我们为$ gl_ {n+m}（f）$定义了Shalika模型的概括，并证明它们是无数次的，其中$ f $是非架构的本地字段或有限的字段，而$ n，m $是任何自然数字。特别是，我们为$ n = m $的情况提供了新的证明。我们还表明，$ gl_n（f）$的不可约代表的伯恩斯坦 - Zelevinsky产品和$ gl_m（f）$的微不足道表示不含多重性。我们通过猜想对Gelfand Pairs的扭曲抛物线诱导来关联这两个结果。
We define a generalization of Shalika models for $GL_{n+m}(F)$ and prove that they are multiplicity-free, where $F$ is either a non-Archimedean local field or a finite field and $n,m$ are any natural numbers. In particular, we give new proof for the case of $n=m$. We also show that the Bernstein-Zelevinsky product of an irreducible representation of $GL_n(F)$ and the trivial representation of $GL_m(F)$ is multiplicity-free. We relate the two results by a conjecture about twisted parabolic induction of Gelfand pairs.
