W-representations carried by the wcells in PGL(4,H) x SU(4,4) block of PGL8

wcell#0:
  cardinality : 14
  special orbit : [4, 4]
  special representation : [4, 4]
  cell representation : phi[4,4]

wcell#1:
  cardinality : 56
  special orbit : [3, 3, 1, 1]
  special representation : [3, 3, 1, 1]
  cell representation : phi[3,3,1,1]

wcell#2:
  cardinality : 14
  special orbit : [2, 2, 2, 2]
  special representation : [2, 2, 2, 2]
  cell representation : phi[2,2,2,2]

wcell#3:
  cardinality : 20
  special orbit : [2, 2, 1, 1, 1, 1]
  special representation : [2, 2, 1, 1, 1, 1]
  cell representation : phi[2,2,1,1,1,1]

wcell#4:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [1, 1, 1, 1, 1, 1, 1, 1]
  cell representation : phi[1,1,1,1,1,1,1,1]