W-representations carried by the wcells in Spin(12,3) x PSp(14,R) block of Spin15

wcell#0:
  cardinality : 50
  special orbit : [7, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[3], [1, 1, 1, 1]]
  cell representation : phi[[3, 1, 1, 1, 1],[]]+phi[[3],[1, 1, 1, 1]]

wcell#1:
  cardinality : 154
  special orbit : [5, 3, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [2, 1, 1, 1]]
  cell representation : phi[[2],[2, 1, 1, 1]]+phi[[1],[3, 1, 1, 1]]

wcell#2:
  cardinality : 105
  special orbit : [3, 3, 3, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [2, 1, 1, 1]]
  cell representation : phi[[1, 1, 1, 1, 1],[2]]+phi[[1, 1],[2, 1, 1, 1]]

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

wcell#4:
  cardinality : 36
  special orbit : [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[2], [1, 1, 1, 1, 1]]
  cell representation : phi[[2],[1, 1, 1, 1, 1]]+phi[[],[3, 1, 1, 1, 1]]

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

wcell#6:
  cardinality : 35
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1, 1]]

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

wcell#8:
  cardinality : 35
  special orbit : [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [2, 1, 1, 1, 1]]
  cell representation : phi[[1],[2, 1, 1, 1, 1]]

wcell#9:
  cardinality : 28
  special orbit : [3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1, 1], [1, 1, 1, 1, 1]]
  cell representation : phi[[1, 1, 1, 1, 1, 1],[1]]+phi[[1, 1],[1, 1, 1, 1, 1]]

wcell#10:
  cardinality : 13
  special orbit : [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
  special representation : [[1], [1, 1, 1, 1, 1, 1]]
  cell representation : phi[[1],[1, 1, 1, 1, 1, 1]]+phi[[],[2, 1, 1, 1, 1, 1]]

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