[GAP Forum] Using repsn package on A5
Vahid Dabbaghian
vdabbagh at sfu.ca
Wed Oct 13 03:51:14 BST 2010
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
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