\\ Left Cell Data for A3   (CC 2012, B. Binegar)
\\
\\ This file contains a table of data for the 10 left cells of the Weyl
\\ group W of A3. 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 : 10 : 0 : [0, 0] : phi[4] : phi[4] : [4] : 0 : 0 : e : 0 : [{{}}, {}]
1 : 10 : 1 : [1, 0] : phi[3,1] : phi[3,1] : [3, 1] : 1 : 0 : 3 : 1 : [{{3}}, {{2}}]
2 : 10 : 2 : [2, 0] : phi[3,1] : phi[3,1] : [3, 1] : 2 : 0 : 2 : 1 : [{{2}}, {{1}, {3}}]
3 : 10 : 3 : [3, 0] : phi[3,1] : phi[3,1] : [3, 1] : 3 : 0 : 1 : 1 : [{{1}}, {{2}}]
4 : 10 : 7 : [4, 0] : phi[2,2] : phi[2,2] : [2, 2] : 7 : 0 : 13 : 2 : [{{1, 3}}, {{2}}]
5 : 10 : 16 : [5, 1] : phi[2,2] : phi[2,2] : [2, 2] : 16 : 1 : 2132 : 2 : [{{2}}, {{1, 3}}]
6 : 10 : 10 : [6, 0] : phi[2,1,1] : phi[2,1,1] : [2, 1, 1] : 10 : 0 : 232 : 3 : [{{2, 3}}, {{1, 3}}]
7 : 10 : 14 : [7, 0] : phi[2,1,1] : phi[2,1,1] : [2, 1, 1] : 14 : 0 : 121 : 3 : [{{1, 2}}, {{1, 3}}]
8 : 10 : 21 : [8, 2] : phi[2,1,1] : phi[2,1,1] : [2, 1, 1] : 21 : 2 : 12321 : 3 : [{{1, 3}}, {{1, 2}, {2, 3}}]
9 : 10 : 23 : [9, 0] : phi[1,1,1,1] : phi[1,1,1,1] : [1, 1, 1, 1] : 23 : 0 : 121321 : 6 : [{{1, 2, 3}}, {}]