Atlas · cell_graph.at · trivial representation

The graph on W-cells, W_cell_graph(p)

Each box is a W-cell in the block of the trivial representation, numbered as in block_of(p) and W_cells(p). Arrows are the Hasse diagram of the order on cells that print_W_cells calls the induced graph. Each cell is labelled by its special nilpotent orbit, the associated variety of the annihilator of its members, obtained from the special representation of the cell by the Springer correspondence. Rows are Gelfand–Kirillov dimension, half the dimension of the orbit, which increases along every arrow. Click a cell to see what lies above and below it.

Group
Arrows

Cells, by GK dimension

selected reachable by arrows: larger AV arrows reach it: smaller AV contains p same orbit as selected

Drag to pan, scroll or use the buttons to zoom. Click empty space to clear the selection.

Orbits

special nilpotent orbits reached by cells, largest first; click a cell to select it

All cells

click a row to select

Reproduce in atlas


      

        
        
        
      

      

      
The .dot text is what W_cell_graph(p) prints. Render it with dot -Tpdf -o cells.pdf cells.dot. GK dimensions come from the special representation of each cell, as in GK_dim in associated_variety_annihilator.at.