78.6 jInductionTable for Macdonald-Lusztig-Spaltenstein induction

jInductionTable( H, W )

computes the decomposition into irreducible characters of W of the j-induced of the irreducible characters of H. The j-induced of chi is the sum of the irreducible components of the induced of chi which have same b-function (see LowestPowerFakeDegrees) as chi. In the table the rows correspond to the characters of the parent group, the columns to those of the subgroup. What is returned is actually a record with several fields: scalar contains the induction table proper, and there is a Display method. The other fields contain labeling information taken from the character tables of H and W when it exists.

    gap> W := CoxeterGroup( "D", 4);;
    gap> H := ReflectionSubgroup( W, [ 1, 3 ] );;
    gap> Display( jInductionTable( H, W ) );
    j-Induction from A2 into D4
          

 111 21 3
    ________________
    11.+  

   .  . .
    11.-  

   .  . .
    1.111 

   .  . .
    .1111 

   .  . .
    11.2  

   .  . .
    1.21  

   1  . .
    .211  

   .  . .
    2.+   

   .  . .
    2.-   

   .  . .
    .22   

   .  . .
    1.3   

   .  1 .
    .31   

   .  . .
    .4    

This function requires the package "chevie" (see RequirePackage).

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