Conductors and newforms for U(1,1)

Details Conductors and newforms for U(1,1) Conductors and newforms for U(1,1)

2005-03-05

arxiv.org/abs/math/0503090v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 319-343

Mathematics

Number Theory

25 pages

Scientific paper

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 $\pi$ of $U(1,1)(F)$, we attach an integer $c(\pi)$ called the conductor of $\pi$, which depends only on the $L$-packet $\Pi$ containing $\pi$. A newform is a vector in $\pi$ which is essentially fixed by a congruence subgroup of level $c(\pi)$. 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.

Affiliated with

Also associated with

No associations

Rating

Conductors and newforms for U(1,1) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conductors and newforms for U(1,1), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conductors and newforms for U(1,1) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257137