Vol. 7, No. 5, 2014

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Matrix coefficients of depth-zero supercuspidal representations of $\mathrm{GL}(2)$

Andrew Knightly and Carl Ragsdale

Vol. 7 (2014), No. 5, 669–690
Abstract

We give explicit formulas for matrix coefficients of the depth-zero supercuspidal representations of GL(2) over a nonarchimedean local field, highlighting the case where the test vector is a unit new vector. We also describe the partition of the set of such representations according to central character, and compute sums of matrix coefficients over all representations in a given class.

Keywords
supercuspidal, matrix coefficients, regular characters
Mathematical Subject Classification 2010
Primary: 22E50
Milestones
Received: 14 August 2013
Revised: 12 November 2013
Accepted: 16 November 2013
Published: 1 August 2014

Communicated by Michael E. Zieve
Authors
Andrew Knightly
Department of Mathematics and Statistics
University of Maine
5752 Neville Hall, Room 333
Orono, ME 04469-5752
United States
Carl Ragsdale
Department of Mathematics and Statistics
University of Maine
5752 Neville Hall, Room 333
Orono, ME 04469-5752
United States