Conductors and newforms for SL(2)
Conductors and newforms for SL(2)
复制标题
SL(2) 的导体和新形式
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
A. Raghuram
中科院分区：
文献类型：
--
作者：
Joshua M. Lansky;A. Raghuram
本文给出了一个关于SL2(F)的新形式理论，其中F是残馀特征为奇的非阿基米德局部域。这类似于Casselman对GL2(F)和Jacquet， Piatetski-Shapiro和Shalika对GLn(F)的研究结果。对于SL2(F)的表示p我们附加一个整数c(p)我们称之为p的导体p的导体只取决于l包？包含p。它等于GL2(F)的最小表示的导体，决定了l包？新形式是p中的向量，它本质上是由层c(p)的同余子群固定的。对于SL2(F)，我们证明了我们的新形式总是一些标准惠特克泛函的测试向量，并且在此过程中，我们给出了新形式的各种显式公式
In this paper we develop a theory of newforms for SL2(F) where F is a nonarchimedean local field whose residue characteristic is odd. This is analogous to results of Casselman for GL2(F) and Jacquet, Piatetski-Shapiro, and Shalika for GLn(F). To a representation p of SL2(F) we attach an integer c(p) that we call the conductor of p. The conductor of p depends only on the L-packet ? containing p. It is shown to be equal to the conductor of a minimal representation of GL2(F) determining the L-packet ?. A newform is a vector in p which is essentially fixed by a congruence subgroup of level c(p). For SL2(F) we show that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit formulae for newforms