W-representations carried by the wcells in Sp(4,4) x SO(9,8) block of Sp16

wcell#0:
  cardinality : 126
  special orbit : [8, 8]
  special representation : [[4], [4]]
  cell representation : phi[[4],[4]]+phi[[3],[5]]

wcell#1:
  cardinality : 224
  special orbit : [7, 7, 1, 1]
  special representation : [[3], [4, 1]]
  cell representation : phi[[3],[4, 1]]

wcell#2:
  cardinality : 224
  special orbit : [7, 7, 1, 1]
  special representation : [[3], [4, 1]]
  cell representation : phi[[3],[4, 1]]

wcell#3:
  cardinality : 1610
  special orbit : [6, 6, 2, 2]
  special representation : [[3, 1], [3, 1]]
  cell representation : phi[[3, 1],[3, 1]]+phi[[2, 1],[4, 1]]+phi[[3],[3, 2]]+phi[[2],[4, 2]]

wcell#4:
  cardinality : 616
  special orbit : [6, 6, 1, 1, 1, 1]
  special representation : [[3], [3, 1, 1]]
  cell representation : phi[[3],[3, 1, 1]]+phi[[2],[4, 1, 1]]

wcell#5:
  cardinality : 560
  special orbit : [5, 5, 3, 3]
  special representation : [[2, 1], [3, 2]]
  cell representation : phi[[2, 1],[3, 2]]

wcell#6:
  cardinality : 1120
  special orbit : [5, 5, 2, 2, 1, 1]
  special representation : [[2, 1], [3, 1, 1]]
  cell representation : phi[[2, 1],[3, 1, 1]]+phi[[2],[3, 2, 1]]

wcell#7:
  cardinality : 560
  special orbit : [5, 5, 3, 3]
  special representation : [[2, 1], [3, 2]]
  cell representation : phi[[2, 1],[3, 2]]

wcell#8:
  cardinality : 420
  special orbit : [4, 4, 4, 4]
  special representation : [[2, 2], [2, 2]]
  cell representation : phi[[2, 2],[2, 2]]+phi[[1, 1],[3, 3]]

wcell#9:
  cardinality : 1008
  special orbit : [4, 4, 3, 3, 1, 1]
  special representation : [[2, 1], [2, 2, 1]]
  cell representation : phi[[2, 1],[2, 2, 1]]+phi[[1, 1],[3, 2, 1]]

wcell#10:
  cardinality : 1120
  special orbit : [5, 5, 2, 2, 1, 1]
  special representation : [[2, 1], [3, 1, 1]]
  cell representation : phi[[2, 1],[3, 1, 1]]+phi[[2],[3, 2, 1]]

wcell#11:
  cardinality : 280
  special orbit : [5, 5, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [3, 1, 1, 1]]
  cell representation : phi[[2],[3, 1, 1, 1]]

wcell#12:
  cardinality : 252
  special orbit : [3, 3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 2, 1, 1]]
  cell representation : phi[[1, 1],[2, 2, 1, 1]]

wcell#13:
  cardinality : 1008
  special orbit : [4, 4, 3, 3, 1, 1]
  special representation : [[2, 1], [2, 2, 1]]
  cell representation : phi[[2, 1],[2, 2, 1]]+phi[[1, 1],[3, 2, 1]]

wcell#14:
  cardinality : 280
  special orbit : [5, 5, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [3, 1, 1, 1]]
  cell representation : phi[[2],[3, 1, 1, 1]]

wcell#15:
  cardinality : 252
  special orbit : [3, 3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 2, 1, 1]]
  cell representation : phi[[1, 1],[2, 2, 1, 1]]

wcell#16:
  cardinality : 1274
  special orbit : [4, 4, 2, 2, 2, 2]
  special representation : [[2, 1, 1], [2, 1, 1]]
  cell representation : phi[[2, 1, 1],[2, 1, 1]]+phi[[1, 1, 1],[3, 1, 1]]+phi[[2],[2, 2, 2]]+phi[[1],[3, 2, 2]]

wcell#17:
  cardinality : 1260
  special orbit : [4, 4, 2, 2, 1, 1, 1, 1]
  special representation : [[2, 1], [2, 1, 1, 1]]
  cell representation : phi[[2, 1],[2, 1, 1, 1]]+phi[[1, 1],[3, 1, 1, 1]]+phi[[2],[2, 2, 1, 1]]+phi[[1],[3, 2, 1, 1]]

wcell#18:
  cardinality : 260
  special orbit : [4, 4, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1, 1, 1]]
  cell representation : phi[[2],[2, 1, 1, 1, 1]]+phi[[1],[3, 1, 1, 1, 1]]

wcell#19:
  cardinality : 420
  special orbit : [3, 3, 3, 3, 2, 2]
  special representation : [[1, 1, 1], [2, 2, 1]]
  cell representation : phi[[1, 1, 1],[2, 2, 1]]+phi[[1, 1],[2, 2, 2]]

wcell#20:
  cardinality : 252
  special orbit : [3, 3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 2, 1, 1]]
  cell representation : phi[[1, 1],[2, 2, 1, 1]]

wcell#21:
  cardinality : 336
  special orbit : [3, 3, 2, 2, 2, 2, 1, 1]
  special representation : [[1, 1, 1], [2, 1, 1, 1]]
  cell representation : phi[[1, 1, 1],[2, 1, 1, 1]]+phi[[1],[2, 2, 2, 1]]

wcell#22:
  cardinality : 252
  special orbit : [3, 3, 2, 2, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1, 1, 1]]+phi[[1],[2, 2, 1, 1, 1]]

wcell#23:
  cardinality : 336
  special orbit : [3, 3, 2, 2, 2, 2, 1, 1]
  special representation : [[1, 1, 1], [2, 1, 1, 1]]
  cell representation : phi[[1, 1, 1],[2, 1, 1, 1]]+phi[[1],[2, 2, 2, 1]]

wcell#24:
  cardinality : 252
  special orbit : [3, 3, 2, 2, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1, 1, 1]]+phi[[1],[2, 2, 1, 1, 1]]

wcell#25:
  cardinality : 84
  special orbit : [2, 2, 2, 2, 2, 2, 2, 2]
  special representation : [[1, 1, 1, 1], [1, 1, 1, 1]]
  cell representation : phi[[1, 1, 1, 1],[1, 1, 1, 1]]+phi[[],[2, 2, 2, 2]]

wcell#26:
  cardinality : 48
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#27:
  cardinality : 48
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1, 1, 1]]

wcell#28:
  cardinality : 84
  special orbit : [2, 2, 2, 2, 2, 2, 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]]+phi[[],[2, 2, 2, 1, 1]]

wcell#29:
  cardinality : 48
  special orbit : [2, 2, 2, 2, 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]]+phi[[],[2, 2, 1, 1, 1, 1]]

wcell#30:
  cardinality : 15
  special orbit : [2, 2, 1, 1, 1, 1, 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]]+phi[[],[2, 1, 1, 1, 1, 1, 1]]

wcell#31:
  cardinality : 1
  special orbit : [1, 1, 1, 1, 1, 1, 1, 1, 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]]