############################################################################# ## ## Partial Brauer table of Th mod 3 ## ## Reading this file into a GAP session creates a record `Thmod3info' ## which contains the relevant information. ## Afterwards, the following works. ## ## gap> Display( Thmod3info.tmod3, rec( chars:= Thmod3info.ibrpart ) ); ## if not LoadPackage( "ctbllib" ) then Error( "the GAP Character Table Library is not available" ); fi; Thmod3info:= rec( text:= JoinStringsWithSeparator( [ "partial Brauer table of Th mod 3,", "constructed by Gerhard Hiss;", "14 irreducible Brauer characters known (component ibrpart),", " 2 missing (upper bounds in component other);", "last change of this file on July 25, 2007", ], "\n" ), t := CharacterTable( "Th" ), tmod3 := CharacterTableRegular( ~.t, 3 ), basicset := [1,2,3,4,6,9,12,13,14,17,19,25,32,42,43,48], ordchars := RestrictedClassFunctions( Irr( ~.t ){ ~.basicset }, ~.tmod3 ), decinv := [ [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,-2,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [-1,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [-1,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0], [0,2,-1,-1,-1,-1,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1] ], ibrpart := List( ~.decinv{ [1,2,3,4,5,6,13,14,7,9,11,15,12,16] } * ~.ordchars, x -> Character( ~.tmod3, x ) ), other := List( ~.decinv{ [8,10] } * ~.ordchars, x -> Character( ~.tmod3, x ) ), );;