Vol. 273, No. 1, 2015

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A theorem of Mœglin and Waldspurger for covering groups

Shiv Prakash Patel

Vol. 273 (2015), No. 1, 225–239
Abstract

Let E be a nonarchimedean local field of characteristic zero and residual characteristic p. Let G be a connected reductive group defined over E and π an irreducible admissible representation of G(E). A result of C. Mœglin and J.-L. Waldspurger (for p2) and S. Varma (for p = 2) states that the leading coefficient in the character expansion of π at the identity element of G(E) gives the dimension of a certain space of degenerate Whittaker forms. In this paper we generalize this result of Mœglin and Waldspurger to the setting of covering groups of G(E).

Keywords
covering groups, character expansion, degenerate Whittaker forms
Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F70, 11S37
Milestones
Received: 10 February 2014
Revised: 13 April 2014
Accepted: 19 April 2014
Published: 6 December 2014
Authors
Shiv Prakash Patel
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Colaba
Mumbai 400005
India