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Stable automorphic forms for the general linear group

Jae-Hyun Yang

Abstract

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

Stable automorphic forms for the general linear group

Abstract

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

Paper Structure

This paper contains 6 sections, 12 theorems, 170 equations.

Table of Contents

  1. Introduction
  2. Review on the geometry of $GL(n,\Bbb R)/O(n,\Bbb R)$
  3. Polarized real tori
  4. The moduli space of polarized real tori
  5. Automorphic forms for $GL(n,\Bbb R)$
  6. Stable automorphic forms for the general linear group

Key Result

Theorem 2.1

A geodesic $\alpha (t)$ joining $I_n$ and $Y\in {\mathscr P}_n$ has the form where is the spectral decomposition of $Y$, where $V\in O(n,\Bbb R),\ A={\rm diag} (a_1,\cdots,a_n)$ with all $a_j\in \Bbb R.$ The distance of $\alpha (t) \ (0\leq t\leq 1)$ between $I_n$ and $Y$ is

Theorems & Definitions (29)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Proposition 2.1
  • proof
  • Theorem 2.3
  • proof
  • Proposition 2.2
  • proof
  • ...and 19 more