\\ Left Cell Data for C3   (CC 2012, B. Binegar)
\\
\\ This file contains a table of data for the 14 left cells of the Weyl
\\ group W of C3. Each line below corresponds to a particular left cell
\\ of W. The datums held in the (colon-delimited) columns are as follows:
\\ Column   Contents
\\     1    KLatlas index (order of discovery by KLatlas, counting from 0)
\\     2    number of Weyl group elements in the left cell
\\     3    Weyl group elements contained in the left cell (as enumerated by KLatlas, counting from 0)
\\     4    KLatlas indices of the left cells immediately below the left cell in the W-graph of W
\\     5    representation of W carried by left cell (in terms of partitions for the classical Weyl groups and
\\          or R. Carter's notation for the irreducible representations of the exceptional Weyl groups)
\\     6    special representation of W attached to the cell
\\     7    special nilpotent orbit attached to the left cell (in terms of partitions for the nilpotent orbits of
\\          classical groups or Bala-Carter notation for the nilpotent orbits of the exceptional groups
\\     8    KLatlas block index of the unique Duflo involution contained in the left cell
\\     9    KLatlas cell index of the unique Duflo involution contained in the left cell
\\    10    reduced word expression for the unique Duflo involution contained in the left cell
\\    11    A-value of the unique Duflo involution contained in the left cell
\\    12    tau-infinity invariant of primitive ideal attached to the left cell
\\
0 : 14 : 0 : [0, 0] : phi[[3],[]] : phi[[3],[]] : [6] : 0 : 0 : e : 0 : [{{}}, {}, {}]
1 : 14 : 1 : [1, 0] : phi[[2, 1],[]]+phi[[2],[1]] : phi[[2],[1]] : [4, 2] : 1 : 0 : 1 : 1 : [{{1}}, {{2}}, {{1}, {3}}]
2 : 14 : 2 : [2, 0] : phi[[2, 1],[]]+phi[[2],[1]] : phi[[2],[1]] : [4, 2] : 2 : 0 : 2 : 1 : [{{2}}, {{1}, {3}}, {{2}}]
3 : 14 : 3 : [3, 0] : phi[[2],[1]]+phi[[],[3]] : phi[[2],[1]] : [4, 2] : 3 : 0 : 3 : 1 : [{{3}}, {{2}}, {{1}, {3}}]
4 : 14 : 7 : [4, 0] : phi[[1],[2]] : phi[[1],[2]] : [3, 3] : 7 : 0 : 31 : 2 : [{{1, 3}}, {{2}}, {{3}, {1, 3}}]
5 : 14 : 18 : [5, 1] : phi[[1],[2]] : phi[[1],[2]] : [3, 3] : 18 : 1 : 2312 : 2 : [{{2}}, {{3}, {1, 3}}, {{2}}]
6 : 14 : 10 : [6, 0] : phi[[1, 1],[1]] : phi[[1, 1],[1]] : [2, 2, 2] : 10 : 0 : 212 : 3 : [{{1, 2}}, {{1, 3}}, {{2}, {1, 2}}]
7 : 14 : 37 : [7, 2] : phi[[1],[2]] : phi[[1],[2]] : [3, 3] : 37 : 2 : 323123 : 2 : [{{3}}, {{2}}, {{3}, {1, 3}}]
8 : 14 : 29 : [8, 1] : phi[[1, 1],[1]] : phi[[1, 1],[1]] : [2, 2, 2] : 29 : 1 : 32123 : 3 : [{{1, 3}}, {{2}, {1, 2}}, {{1, 3}}]
9 : 14 : 40 : [9, 2] : phi[[1, 1],[1]] : phi[[1, 1],[1]] : [2, 2, 2] : 40 : 2 : 2321232 : 3 : [{{2}}, {{1, 3}}, {{2}, {1, 2}}]
10 : 14 : 23 : [10, 0] : phi[[1],[1, 1]]+phi[[],[2, 1]] : phi[[1],[1, 1]] : [2, 2, 1, 1] : 23 : 0 : 3232 : 4 : [{{2, 3}}, {{1, 3}}, {{1, 2}, {2, 3}}]
11 : 14 : 35 : [11, 1] : phi[[1],[1, 1]]+phi[[],[2, 1]] : phi[[1],[1, 1]] : [2, 2, 1, 1] : 35 : 1 : 312321 : 4 : [{{1, 3}}, {{1, 2}, {2, 3}}, {{1, 3}}]
12 : 14 : 44 : [12, 3] : phi[[1, 1, 1],[]]+phi[[1],[1, 1]] : phi[[1],[1, 1]] : [2, 2, 1, 1] : 44 : 3 : 23212321 : 4 : [{{1, 2}}, {{1, 3}}, {{1, 2}, {2, 3}}]
13 : 14 : 47 : [13, 0] : phi[[],[1, 1, 1]] : phi[[],[1, 1, 1]] : [1, 1, 1, 1, 1, 1] : 47 : 0 : 323212321 : 9 : [{{1, 2, 3}}, {}, {}]