[GAP Forum] Using repsn package on A5

[Vahid Dabbaghian]

Krishna, 

Whenever IrreucibleAffordingRepresentation needs to extend a representation, an Info message appears first. See the following example. 

gap> m:=AllPrimitiveGroups(DegreeOperation,81,IsSolvable,true);; 
gap> G:=m[30];; 
gap> chi := Irr(G)[8];; 
gap> rep := IrreducibleAffordingRepresentation(chi);; 
#I Need to extend a representation of degree 2. This may take a while. 

Vahid 
____________________________________________ 
Program Director 
Modelling of Complex Social Systems (MoCSSy) 
The IRMACS Centre (ASB 10905) 
Simon Fraser University, BC Canada 
Tel: 778-782-7854 
http://mocssy.irmacs.sfu.ca/ 


From: "krishna mohan" <trebauchet1986 at yahoo.co.in> 
To: "Vahid Dabbaghian" <vdabbagh at sfu.ca> 
Cc: "gap forum" <forum at gap-system.org> 
Sent: Tuesday, October 12, 2010 7:05:39 PM 
Subject: Re: [GAP Forum] Using repsn package on A5 


Thanks Vahid, 
Just one more quick question...so is there a way to know, for a particular group and character, whether repsn is extending a representation or not (i.e for the command IrreucibleAffordingRepresentation)? 

Krishna 



From: Vahid Dabbaghian <vdabbagh at sfu.ca> 
To: krishna mohan <trebauchet1986 at yahoo.co.in> 
Cc: gap forum <forum at gap-system.org> 
Sent: Tue, 12 October, 2010 9:01:21 AM 
Subject: Re: [GAP Forum] Using repsn package on A5 


Dear Krishna, 

The answer to your question is yes. You may get different representations for different trials even for solvable groups. For solvable groups, the only case that you will get the same answer is when it doesn't need to extend a representation. 

I hope it helps. 

Regards 
Vahid 

____________________________________________ 
Program Director 
Modelling of Complex Social Systems (MoCSSy) 
The IRMACS Centre (ASB 10905) 
Simon Fraser University, BC Canada 
Tel: 778-782-7854 
http://mocssy.irmacs.sfu.ca/ 

----- Original Message ----- 
From: "krishna mohan" < trebauchet1986 at yahoo.co.in > 
To: "gap forum" < forum at gap-system.org > 
Sent: Sunday, October 10, 2010 5:29:01 AM 
Subject: [GAP Forum] Using repsn package on A5 

Hi.... 

I do the following: 

gap> g:=AllSmallGroups(60)[5]; 
Group([ (1,2,3,4,5), (1,2,3) ]) 

gap> StructureDescription(g); 
"A5" 

gap> LoadPackage("repsn"); 
true 

gap> chi:=Irr(g);; 

gap> rep1:=IrreducibleAffordingRepresentation(chi[4]); 
[ (1,2)(3,4), (1,4)(2,3), (1,3)(4,5) ] -> 
[ [ [ E(3), -1/2*E(3)^2, -1/2*E(3)+1/2*E(3)^2, 1/2*E(3)^2 ], [ 1, -E(3), E(3)^2, 
-E(3)^2 ], [ E(3), 1/2*E(3), 1/2*E(3)^2, -1/2*E(3) ], 

[ E(3), -E(3)-1/2*E(3)^2, -3/2*E(3)-1/2*E(3)^2, -1/2*E(3)^2 ] ], 
[ [ E(3)^2, 1/2*E(3), E(3)-1/2*E(3)^2, -1/2*E(3) ], [ 0, -1/2*E(3), 
-E(3)-1/2*E(3)^2, -1/2*E(3)-E(3)^2 ], 

[ E(3)^2, -1/2*E(3)^2, 1/2*E(3)-1/2*E(3)^2, 1/2*E(3)^2 ], [ 1, 
-E(3)-1/2*E(3)^2, -1/2, -1/2*E(3)^2 ] ], 

[ [ 1, -1/2*E(3)+1/2*E(3)^2, 1/2*E(3)+E(3)^2, 1/2*E(3)-1/2*E(3)^2 ], [ 0, -1, 
-1, -E(3) ], [ 0, 0, 0, E(3) ], [ 0, 0, E(3)^2, 0 ] ] ] 

gap> rep2:=IrreducibleAffordingRepresentation(chi[4]); 
[ (1,2)(3,4), (1,4)(2,3), (1,3)(4,5) ] -> 
[ [ [ 1/2*E(3), -1/2*E(3)-E(3)^2, E(3)^2, 1/2*E(3)^2 ], [ 0, -E(3)^2, E(3)^2, 
E(3) ], [ E(3)+1/2*E(3)^2, -3/2*E(3)^2, E(3)^2, 1/2*E(3)-1/2*E(3)^2 ], 

[ 1/2*E(3)-1/2*E(3)^2, -1/2*E(3)+1/2*E(3)^2, 0, -1/2*E(3) ] ], 
[ [ -1/2, 1/2, E(3), -1/2*E(3)-E(3)^2 ], [ 1/2*E(3)+E(3)^2, 1/2*E(3), 1, 
-1/2*E(3)^2 ], [ 1/2*E(3)+E(3)^2, -1/2*E(3)-E(3)^2, 0, -1/2*E(3)^2 ], 

[ -1/2*E(3)-E(3)^2, -3/2*E(3), E(3), -E(3)-1/2*E(3)^2 ] ], 
[ [ -1/2*E(3), 1/2*E(3)+E(3)^2, 0, E(3)+1/2*E(3)^2 ], [ 1/2*E(3), -1/2*E(3), 
E(3), -1/2*E(3)^2 ], [ -1/2*E(3)^2, -E(3)+1/2*E(3)^2, E(3), 1/2 ], 

[ E(3)^2, -1, 1, 0 ] ] ] 


As one can see, the representation matrices are different in the two instances. 
I tried this with a couple of other groups, but always got the same 
representation matrices. 

On going through the repsn manual, it seemed to me that this must be due to the 
fact that A5 is not solvable. 

So, if the group is solvable, then does the program always give the same 
representation matrices? 
Or is it that the matrices generated may be different for different trials even 
for a solvable group? 

Krishnamohan P 


_______________________________________________ 
Forum mailing list 
Forum at mail.gap-system.org 
http://mail.gap-system.org/mailman/listinfo/forum