W-representations carried by the wcells in U(4,4) x GL(4,H) block of GL8

wcell#0:
  cardinality : 1
  special orbit : [8]
  special representation : [8]
  cell representation : phi[8]

wcell#1:
  cardinality : 20
  special orbit : [6, 2]
  special representation : [6, 2]
  cell representation : phi[6,2]

wcell#2:
  cardinality : 14
  special orbit : [4, 4]
  special representation : [4, 4]
  cell representation : phi[4,4]

wcell#3:
  cardinality : 56
  special orbit : [4, 2, 2]
  special representation : [4, 2, 2]
  cell representation : phi[4,2,2]

wcell#4:
  cardinality : 14
  special orbit : [2, 2, 2, 2]
  special representation : [2, 2, 2, 2]
  cell representation : phi[2,2,2,2]