Conductors and newforms for U(1,1)
| dc.creator | Lansky, Joshua | |
| dc.creator | Raghuram, A | |
| dc.date | 2005-03-05 | |
| dc.date.accessioned | 2026-07-07T05:17:41Z | |
| dc.date.available | 2026-07-07T05:17:41Z | |
| dc.description | Let $F$ be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms for $U(1,1)(F)$, building on previous work on $SL_2(F)$. This theory is analogous to the results of Casselman for $GL_2(F)$ and Jacquet, Piatetski-Shapiro, and Shalika for $GL_n(F)$. To a representation $π$ of $U(1,1)(F)$, we attach an integer $c(π)$ called the conductor of $π$, which depends only on the $L$-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. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503090 | |
| dc.identifier | http://arxiv.org/abs/math/0503090 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 319-343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74395 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.title | Conductors and newforms for U(1,1) | |
| dc.type | text |