The Heisenberg group in Complex variables is the Group of all with
and having multiplication
where is the conjugate transpose. The Heisenberg group is Isomorphic to the group of
Every finite-dimensional unitary representation is trivial on and therefore factors to a Representation
of the quotient .
See also Nil Geometry
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.
© 1996-9 Eric W. Weisstein