## Heisenberg Group

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 Matrices

and satisfies

Every finite-dimensional unitary representation is trivial on and therefore factors to a Representation of the quotient .

References

Knapp, A. W. Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.