Conductors and newforms for U(1,1)

Lansky, Joshua ; Raghuram, A. (2004) Conductors and newforms for U(1,1) Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 114 (4). pp. 319-343. ISSN 0253-4142


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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 on SL2(F). This theory is analogous to the results of Casselman for GL2(F) and Jacquet, Piatetski-Shapiro, and Shalika for GLn(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.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Conductor; Newforms; Representations; U(1, 1)
ID Code:106307
Deposited On:01 Feb 2018 17:01
Last Modified:01 Feb 2018 17:01

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