W-representations carried by the wcells in PSp(3,3) x Spin(7,6) block of PSp12

wcell#0:
  cardinality : 25
  special orbit : [6, 6]
  special representation : [[3], [3]]
  cell representation : phi[[3, 3],[]]+phi[[3],[3]]

wcell#1:
  cardinality : 45
  special orbit : [5, 5, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#2:
  cardinality : 145
  special orbit : [4, 4, 2, 2]
  special representation : [[2, 1], [2, 1]]
  cell representation : phi[[2, 2],[1, 1]]+phi[[2, 1],[2, 1]]+phi[[1],[3, 2]]+phi[[],[3, 3]]

wcell#3:
  cardinality : 54
  special orbit : [4, 4, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2, 2, 1, 1],[]]+phi[[2],[2, 1, 1]]

wcell#4:
  cardinality : 30
  special orbit : [3, 3, 3, 3]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#5:
  cardinality : 30
  special orbit : [3, 3, 3, 3]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#6:
  cardinality : 75
  special orbit : [3, 3, 2, 2, 1, 1]
  special representation : [[1, 1], [2, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]

wcell#7:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#8:
  cardinality : 35
  special orbit : [2, 2, 2, 2, 2, 2]
  special representation : [[1, 1, 1], [1, 1, 1]]
  cell representation : phi[[1, 1, 1, 1],[1, 1]]+phi[[1, 1, 1],[1, 1, 1]]

wcell#9:
  cardinality : 24
  special orbit : [2, 2, 2, 2, 1, 1, 1, 1]
  special representation : [[1, 1], [1, 1, 1, 1]]
  cell representation : phi[[1, 1],[1, 1, 1, 1]]+phi[[],[2, 2, 1, 1]]

wcell#10:
  cardinality : 24
  special orbit : [2, 2, 2, 2, 1, 1, 1, 1]
  special representation : [[1, 1], [1, 1, 1, 1]]
  cell representation : phi[[1, 1],[1, 1, 1, 1]]+phi[[],[2, 2, 1, 1]]

wcell#11:
  cardinality : 7
  special orbit : [2, 2, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [1, 1, 1, 1, 1]]
  cell representation : phi[[1, 1, 1, 1, 1, 1],[]]+phi[[1],[1, 1, 1, 1, 1]]

wcell#12:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[1, 1, 1, 1, 1, 1]]

wcell#13:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[], [1, 1, 1, 1, 1, 1]]
  cell representation : phi[[],[1, 1, 1, 1, 1, 1]]