A characterisation of the Fourier transform on the Heisenberg group
  The aim of this paper is to show that any continuous *-homomorphism of L1(Cn)(with twisted convolution as multipli- cation) into B(L2(Rn)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution. 
R. Lakshmi Lavanya and S. Thangavelu
math.FA