To find Brauer Character for the special linear group SL(2,5) in GAP.
$begingroup$
As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $S5$. It worked for me as
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
But i tried same for Special linear group $SL(2,5)$, it does not works
gap> LoadPackage("ctbllib");
true
gap> m:=SL(2,5);
SL(2,5)
gap> t:=CharacterTable("m") mod 2;
fail
gap>
Where is problem. Please help. Thanks.
group-theory gap
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
$endgroup$
|
show 2 more comments
$begingroup$
As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $S5$. It worked for me as
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
But i tried same for Special linear group $SL(2,5)$, it does not works
gap> LoadPackage("ctbllib");
true
gap> m:=SL(2,5);
SL(2,5)
gap> t:=CharacterTable("m") mod 2;
fail
gap>
Where is problem. Please help. Thanks.
group-theory gap
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
$endgroup$
1
$begingroup$
The package did load. It returnedtrue.
$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
1
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
1
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45
|
show 2 more comments
$begingroup$
As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $S5$. It worked for me as
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
But i tried same for Special linear group $SL(2,5)$, it does not works
gap> LoadPackage("ctbllib");
true
gap> m:=SL(2,5);
SL(2,5)
gap> t:=CharacterTable("m") mod 2;
fail
gap>
Where is problem. Please help. Thanks.
group-theory gap
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
$endgroup$
As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $S5$. It worked for me as
gap> t:=CharacterTable("S5") mod 3;
BrauerTable( "A5.2", 3 )
gap> Irr(t);
[ Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, 1, 1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 1, 1, 1, -1, -1 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 6, -2, 1, 0, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, 2, 0 ] ),
Character( BrauerTable( "A5.2", 3 ), [ 4, 0, -1, -2, 0 ] ) ]
But i tried same for Special linear group $SL(2,5)$, it does not works
gap> LoadPackage("ctbllib");
true
gap> m:=SL(2,5);
SL(2,5)
gap> t:=CharacterTable("m") mod 2;
fail
gap>
Where is problem. Please help. Thanks.
group-theory gap
group-theory gap
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
edited Dec 25 '18 at 8:47
neelkanth
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
asked Dec 25 '18 at 7:41
neelkanthneelkanth
2,29321129
2,29321129
1
$begingroup$
The package did load. It returnedtrue.
$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
1
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
1
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45
|
show 2 more comments
1
$begingroup$
The package did load. It returnedtrue.
$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
1
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
1
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45
1
1
$begingroup$
The package did load. It returned
true.$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
The package did load. It returned
true.$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
1
1
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
1
1
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45
|
show 2 more comments
1 Answer
1
active
oldest
votes
$begingroup$
You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.
The ATLAS name of $SL(2,5)$ is 2.L2(5), indeed we can get the table for it as
gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )
Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
$endgroup$
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
|
show 2 more comments
Your Answer
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1 Answer
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$begingroup$
You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.
The ATLAS name of $SL(2,5)$ is 2.L2(5), indeed we can get the table for it as
gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )
Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
$endgroup$
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
|
show 2 more comments
$begingroup$
You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.
The ATLAS name of $SL(2,5)$ is 2.L2(5), indeed we can get the table for it as
gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )
Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
$endgroup$
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
|
show 2 more comments
$begingroup$
You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.
The ATLAS name of $SL(2,5)$ is 2.L2(5), indeed we can get the table for it as
gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )
Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
$endgroup$
You are mixing up the (string) names of groups in the library and variables you choose to assign a group to. The group "M" in the libary is the monster simple group, and for it the Brauer table is not known.
The ATLAS name of $SL(2,5)$ is 2.L2(5), indeed we can get the table for it as
gap> t:=CharacterTable("2.L2(5)") mod 3;
BrauerTable( "2.A5", 3 )
Note that all of this is about pre-computed Brauer tables from the character table library. If you wanted to compute the Brauer table for an arbitrary finite group, you would have to find all irreducible modules (e.g. by splitting up the regular module), and then lift the Brauer character values appropriately (there currently is no pre-defined function which does so automatically).
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
answered Dec 25 '18 at 9:06
ahulpkeahulpke
7,2021026
7,2021026
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
|
show 2 more comments
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Ok thanks sir.... i will try this way and will tell you .....
$endgroup$
– neelkanth
Dec 25 '18 at 9:18
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
Yes Sir now it is working....thanks...
$endgroup$
– neelkanth
Dec 25 '18 at 9:22
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
$begingroup$
But How i will know in future about The ATLAS name of any other group....
$endgroup$
– neelkanth
Dec 25 '18 at 9:23
1
1
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@neelkanth If you are working with simple groups and their relatives, you might want to read through the preface of the ATLAS, as these names have become kind of standard. If you require the Brauer tables for other groups (and need to compute from scratch) I recommend the textbook by Lux and Pahlings published by Cambridge U.P. which contains GAP examples.
$endgroup$
– ahulpke
Dec 25 '18 at 9:57
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
$begingroup$
@ahulpkr thanks sir I will purchase this book ...
$endgroup$
– neelkanth
Dec 25 '18 at 12:27
|
show 2 more comments
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1
$begingroup$
The package did load. It returned
true.$endgroup$
– Shaun
Dec 25 '18 at 8:43
$begingroup$
@Shaun Thanks for edit...
$endgroup$
– neelkanth
Dec 25 '18 at 8:43
$begingroup$
@Shaun But not working to find Brauer Character...
$endgroup$
– neelkanth
Dec 25 '18 at 8:44
1
$begingroup$
I don't know how to fix that, @neelkanth; I'm just saying that the problem doesn't seem to be with the package loading, as the title suggests.
$endgroup$
– Shaun
Dec 25 '18 at 8:45
1
$begingroup$
ok then i change the title....
$endgroup$
– neelkanth
Dec 25 '18 at 8:45