Conductors and newforms for U(1,1) |
| |
Authors: | Email author" target="_blank">Joshua?LanskyEmail author A?Raghuram |
| |
Institution: | (1) Department of Mathematics, American University, 20910 Washington DC, USA;(2) Department of Mathematics, University of Iowa, 14 Maclean Hall, 52242 Iowa City, IA, USA |
| |
Abstract: | Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms
forU (1, 1)(F), building on previous work onSL
2(F). This theory is analogous to the results of Casselman forGL
2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL
n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). 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. |
| |
Keywords: | Conductor newforms representations U(1 1) |
本文献已被 SpringerLink 等数据库收录! |
|