The notion of wave front set has been introduced to p-adic analysis by D. B. Heifetz in 1985.
In this paper we show that for p-adic groups the notion of the wave front set of a representation coincides with the notion of the asymptotic support of its character. For real groups this has been conjectured by Barbasch and Vogan, and was proven by Rossmann in 1993.

Appeared in Pac. J. Math.141, 383--389 (1990)