{
  "id": "math/0503090",
  "version": "v1",
  "published": "2005-03-05T08:44:57.000Z",
  "updated": "2005-03-05T08:44:57.000Z",
  "title": "Conductors and newforms for U(1,1)",
  "authors": [
    "Joshua Lansky",
    "A Raghuram"
  ],
  "comment": "25 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 319-343",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-05T08:44:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-archimedean local field",
      "standard whittaker functionals",
      "explicit formulae",
      "congruence subgroup",
      "test vectors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3090L"
    }
  }
}