Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local Transfer and Reducibility of Induced Representations of $p$-adic Groups of Classical Type

Mahdi Asgari, James W. Cogdell, Freydoon Shahidi

Abstract

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in terms of local functorial transfers of the generic representations of the groups we consider. The existence of the local transfers follows from global generic transfers that were established earlier.

Local Transfer and Reducibility of Induced Representations of $p$-adic Groups of Classical Type

Abstract

We analyze reducibility points of representations of -adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in terms of local functorial transfers of the generic representations of the groups we consider. The existence of the local transfers follows from global generic transfers that were established earlier.

Paper Structure

This paper contains 10 sections, 12 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Local Representations and $L$-functions
  3. Notation
  4. The Langlands-Shahidi Local $L$-functions
  5. Intertwining Operators
  6. Generic Local Transfers - Supercuspidal Case
  7. Reducibility of Local Representations
  8. Reducibility on the Unitary Axis
  9. Reducibility off the Unitary Axis
  10. Reducibility for Groups of Classical Type

Key Result

Theorem 2.13

Assume that ${\bf P}$ is a self-associate maximal parabolic and let $\tau$ be generic, unitary, supercuspidal. Then is a holomorphic, non-vanishing operator on all of $\mathbb C.$

Theorems & Definitions (19)

  • Remark 2.4
  • Theorem 2.13
  • Corollary 2.14
  • Definition 3.1
  • Theorem 3.2
  • proof
  • Definition 4.11
  • Theorem 4.12
  • proof
  • Remark 4.16
  • ...and 9 more