In addition to the representation as real 3x3 matricies, the continuous Heisenberg group also has a representation where it acts on holomorphic functions on the upper half-plane, known as the theta representation, due to its connection with the theta functions.
The continuous Heisenberg group also has a representation where it acts on holomorphic functions on the upper half-plane. This is in addition to the representation as real 3x3 matricies. Plane is due to its connection with the theta functions. Plane is known as the theta representation.