Nilpotent Group Case
Let G be a connected, simply connected nilpotent Lie group. Kirillov proved that the equivalence classes of irreducible unitary representations of G are parametrized by the coadjoint orbits of G, that is the orbits of the action G on the dual space of its Lie algebra. The Kirillov character formula expresses the Harish-Chandra character of the representation as a certain integral over the corresponding orbit.
Read more about this topic: Orbit Method
Famous quotes containing the words group and/or case:
“I can’t think of a single supposedly Black issue that hasn’t wasted the original Black target group and then spread like the measles to outlying white experience.”
—June Jordan (b. 1936)
“What we need to know in any case is very simple.”
—Henry David Thoreau (1817–1862)