#### 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 $\pi$ an irreducible admissible representation of $G\left(E\right)$. A result of C. Mœglin and J.-L. Waldspurger (for $p\ne 2$) and S. Varma (for $p=2$) states that the leading coefficient in the character expansion of $\pi$ at the identity element of $G\left(E\right)$ 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 $G\left(E\right)$.

##### Keywords
covering groups, character expansion, degenerate Whittaker forms
##### Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F70, 11S37