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We introduce a new notion of rank for unitary representations of semisimplegroups over a local field of characteristic zero. The theory is based onKirillov's method of orbits for nilpotent groups over local fields. When thesemisimple group is classical, we prove that the new theory is essentiallyequivalent to Howe's theory of N-rank.

A notion of rank for unitary representations of reductive groups based on Kirillov's orbit method