W-representations carried by the wcells in Spin(8,5) x PSp(12,R) block of Spin13

wcell#0:
  cardinality : 11
  special orbit : [11, 1, 1]
  special representation : [[5], [1]]
  cell representation : phi[[5, 1],[]]+phi[[5],[1]]

wcell#1:
  cardinality : 21
  special orbit : [9, 3, 1]
  special representation : [[4], [2]]
  cell representation : phi[[4],[2]]+phi[[1],[5]]

wcell#2:
  cardinality : 25
  special orbit : [7, 5, 1]
  special representation : [[3], [3]]
  cell representation : phi[[3, 3],[]]+phi[[3],[3]]

wcell#3:
  cardinality : 60
  special orbit : [7, 3, 3]
  special representation : [[3, 1], [2]]
  cell representation : phi[[3, 1],[2]]+phi[[1, 1],[4]]

wcell#4:
  cardinality : 25
  special orbit : [9, 1, 1, 1, 1]
  special representation : [[4], [1, 1]]
  cell representation : phi[[4, 1, 1],[]]+phi[[4],[1, 1]]

wcell#5:
  cardinality : 60
  special orbit : [7, 3, 3]
  special representation : [[3, 1], [2]]
  cell representation : phi[[3, 1],[2]]+phi[[1, 1],[4]]

wcell#6:
  cardinality : 20
  special orbit : [9, 1, 1, 1, 1]
  special representation : [[4], [1, 1]]
  cell representation : phi[[4],[1, 1]]+phi[[],[5, 1]]

wcell#7:
  cardinality : 64
  special orbit : [7, 3, 1, 1, 1]
  special representation : [[3], [2, 1]]
  cell representation : phi[[3],[2, 1]]+phi[[1],[4, 1]]

wcell#8:
  cardinality : 56
  special orbit : [7, 3, 1, 1, 1]
  special representation : [[3], [2, 1]]
  cell representation : phi[[3, 2, 1],[]]+phi[[3],[2, 1]]

wcell#9:
  cardinality : 64
  special orbit : [7, 3, 1, 1, 1]
  special representation : [[3], [2, 1]]
  cell representation : phi[[3],[2, 1]]+phi[[1],[4, 1]]

wcell#10:
  cardinality : 81
  special orbit : [7, 2, 2, 1, 1]
  special representation : [[3, 1], [1, 1]]
  cell representation : phi[[3, 1, 1],[1]]+phi[[3, 1],[1, 1]]

wcell#11:
  cardinality : 45
  special orbit : [5, 5, 1, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#12:
  cardinality : 190
  special orbit : [5, 3, 3, 1, 1]
  special representation : [[2, 1], [2, 1]]
  cell representation : phi[[2, 1, 1],[2]]+phi[[1, 1, 1],[3]]+phi[[2, 1],[2, 1]]+phi[[1, 1],[3, 1]]

wcell#13:
  cardinality : 35
  special orbit : [7, 5, 1]
  special representation : [[3], [3]]
  cell representation : phi[[3],[3]]+phi[[2],[4]]

wcell#14:
  cardinality : 40
  special orbit : [5, 5, 3]
  special representation : [[2, 1], [3]]
  cell representation : phi[[2, 1],[3]]

wcell#15:
  cardinality : 64
  special orbit : [7, 3, 1, 1, 1]
  special representation : [[3], [2, 1]]
  cell representation : phi[[3],[2, 1]]+phi[[1],[4, 1]]

wcell#16:
  cardinality : 45
  special orbit : [5, 5, 1, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#17:
  cardinality : 185
  special orbit : [5, 3, 3, 1, 1]
  special representation : [[2, 1], [2, 1]]
  cell representation : phi[[2, 1],[2, 1]]+phi[[1, 1],[3, 1]]+phi[[2],[2, 2]]+phi[[1],[3, 2]]

wcell#18:
  cardinality : 45
  special orbit : [5, 5, 1, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#19:
  cardinality : 30
  special orbit : [3, 3, 3, 3, 1]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#20:
  cardinality : 30
  special orbit : [3, 3, 3, 3, 1]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#21:
  cardinality : 30
  special orbit : [7, 1, 1, 1, 1, 1, 1]
  special representation : [[3], [1, 1, 1]]
  cell representation : phi[[3],[1, 1, 1]]+phi[[],[4, 1, 1]]

wcell#22:
  cardinality : 54
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2, 2, 1, 1],[]]+phi[[2],[2, 1, 1]]

wcell#23:
  cardinality : 45
  special orbit : [5, 5, 1, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#24:
  cardinality : 185
  special orbit : [5, 3, 3, 1, 1]
  special representation : [[2, 1], [2, 1]]
  cell representation : phi[[2, 1],[2, 1]]+phi[[1, 1],[3, 1]]+phi[[2],[2, 2]]+phi[[1],[3, 2]]

wcell#25:
  cardinality : 30
  special orbit : [7, 1, 1, 1, 1, 1, 1]
  special representation : [[3], [1, 1, 1]]
  cell representation : phi[[3],[1, 1, 1]]+phi[[],[4, 1, 1]]

wcell#26:
  cardinality : 81
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2],[2, 1, 1]]+phi[[1],[3, 1, 1]]

wcell#27:
  cardinality : 81
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2],[2, 1, 1]]+phi[[1],[3, 1, 1]]

wcell#28:
  cardinality : 81
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2],[2, 1, 1]]+phi[[1],[3, 1, 1]]

wcell#29:
  cardinality : 64
  special orbit : [5, 2, 2, 1, 1, 1, 1]
  special representation : [[2, 1], [1, 1, 1]]
  cell representation : phi[[2, 1, 1, 1],[1]]+phi[[2, 1],[1, 1, 1]]

wcell#30:
  cardinality : 75
  special orbit : [3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]

wcell#31:
  cardinality : 25
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [1, 1, 1, 1]]
  cell representation : phi[[2],[1, 1, 1, 1]]+phi[[],[3, 1, 1, 1]]

wcell#32:
  cardinality : 45
  special orbit : [5, 5, 1, 1, 1]
  special representation : [[2], [3, 1]]
  cell representation : phi[[2],[3, 1]]

wcell#33:
  cardinality : 81
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2],[2, 1, 1]]+phi[[1],[3, 1, 1]]

wcell#34:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#35:
  cardinality : 30
  special orbit : [3, 3, 3, 3, 1]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#36:
  cardinality : 40
  special orbit : [3, 3, 3, 2, 2]
  special representation : [[1, 1, 1], [2, 1]]
  cell representation : phi[[1, 1, 1],[2, 1]]

wcell#37:
  cardinality : 40
  special orbit : [3, 3, 3, 2, 2]
  special representation : [[1, 1, 1], [2, 1]]
  cell representation : phi[[1, 1, 1],[2, 1]]

wcell#38:
  cardinality : 81
  special orbit : [5, 3, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1]]
  cell representation : phi[[2],[2, 1, 1]]+phi[[1],[3, 1, 1]]

wcell#39:
  cardinality : 75
  special orbit : [3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]

wcell#40:
  cardinality : 56
  special orbit : [5, 2, 2, 1, 1, 1, 1]
  special representation : [[2, 1], [1, 1, 1]]
  cell representation : phi[[2, 1],[1, 1, 1]]+phi[[],[3, 2, 1]]

wcell#41:
  cardinality : 75
  special orbit : [3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]

wcell#42:
  cardinality : 35
  special orbit : [3, 2, 2, 2, 2, 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#43:
  cardinality : 30
  special orbit : [3, 3, 3, 3, 1]
  special representation : [[1, 1], [2, 2]]
  cell representation : phi[[1, 1],[2, 2]]

wcell#44:
  cardinality : 25
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [1, 1, 1, 1]]
  cell representation : phi[[2],[1, 1, 1, 1]]+phi[[],[3, 1, 1, 1]]

wcell#45:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#46:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#47:
  cardinality : 75
  special orbit : [3, 3, 3, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1]]
  cell representation : phi[[1, 1],[2, 1, 1]]+phi[[1],[2, 2, 1]]

wcell#48:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#49:
  cardinality : 24
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1]]

wcell#50:
  cardinality : 24
  special orbit : [3, 2, 2, 1, 1, 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#51:
  cardinality : 11
  special orbit : [3, 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]]+phi[[],[2, 1, 1, 1, 1]]

wcell#52:
  cardinality : 24
  special orbit : [3, 2, 2, 1, 1, 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#53:
  cardinality : 11
  special orbit : [3, 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]]+phi[[],[2, 1, 1, 1, 1]]

wcell#54:
  cardinality : 1
  special orbit : [1, 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]]