CharTableCollapsedClasses( tbl, fusionmap )
returns a character table where all classes of the character table tbl
with equal images under the map fusionmap are collapsed;
the fields orders
, classes
, and the characters in irreducibles
are
the images under fusionmap, the powermaps are obtained on conjugation
(see TransferDiagram) with fusionmap, order
remains unchanged,
and centralizers
arise from classes
and order
.
The fusion to the returned table is stored on tbl.
gap> c3:= CharTable( "Cyclic", 3 );; gap> t:= CharTableSplitClasses( c3, [ 1, 2, 2, 3, 3 ] );; gap> PrintCharTable( t ); rec( identifier := "Split(C3,[ 1, 2, 2, 3, 3 ])", size := 3, order := 3, name := "Split(C3,[ 1, 2, 2, 3, 3 ])", centralizers := [ 3, 6, 6, 6, 6 ], classes := [ 1, 1/2, 1/2, 1/2, 1/2 ], orders := [ 1, 3, 3, 3, 3 ], powermap := [ ,, [ 1, 1, 1, 1, 1 ] ], irreducibles := [ [ 1, 1, 1, 1, 1 ], [ 1, E(3), E(3), E(3)^2, E(3)^2 ], [ 1, E(3)^2, E(3)^2, E(3), E(3) ] ], fusions := [ rec( name := [ 'C', '3' ], map := [ 1, 2, 2, 3, 3 ] ) ], operations := CharTableOps ) gap> c:= CharTableCollapsedClasses( t, [ 1, 2, 2, 3, 3 ] );; gap> PrintCharTable( c ); rec( identifier := "Collapsed(Split(C3,[ 1, 2, 2, 3, 3 ]),[ 1, 2, 2, 3\ , 3 ])", size := 3, order := 3, name := "Collapsed(Split(C3,[ 1, 2, 2, 3, 3 ]),[ 1, 2, 2, 3, 3 ])",\ centralizers := [ 3, 3, 3 ], orders := [ 1, 3, 3 ], powermap := [ ,, [ 1, 1, 1 ] ], fusionsource := [ "Split(C3,[ 1, 2, 2, 3, 3 ])" ], irreducibles := [ [ 1, 1, 1 ], [ 1, E(3), E(3)^2 ], [ 1, E(3)^2, E(3) ] ], classes := [ 1, 1, 1 ], operations := CharTableOps )
The inverse process of fusion is the splitting of classes, see CharTableSplitClasses.
GAP 3.4.4