A lower bound for the canonical dimension of depth-zero supercuspidal representations

The canonical dimension is an invariant attached to complex admissible representations of p-adic reductive groups that has not received significant attention so far and which is closely related to the wavefront set. We find a new lower bound for the canonical dimension of depth-zero supercuspidal representations. This lower bound is uniform in the sense that it only depends on the group and not on the representation itself. This lower bound effectively provides a lower bound for the corresponding wavefront set. In order to obtain this result, we first generalize a result on the asymptotic growth of the cardinality of balls in the Bruhat-Tits building to the case of exceptional types.