To find Brauer Character for the special linear group SL(2,5) in GAP.
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 2 hours ago
neelkanth
2,0611927
|
show 1 more comment
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 2 hours ago
neelkanth
2,0611927
1
The package did load. It returnedtrue.
– Shaun
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
1
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.
– Shaun
1 hour ago
1
ok then i change the title....
– neelkanth
1 hour ago
|
show 1 more comment
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 2 hours ago
neelkanth
2,0611927
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 2 hours ago
neelkanth
2,0611927
asked 2 hours ago
neelkanth
2,0611927
edited 1 hour ago
asked 2 hours ago
neelkanth
2,0611927
asked 2 hours ago
neelkanth
2,0611927
asked 2 hours ago
neelkanth
2,0611927
2,0611927
1
The package did load. It returnedtrue.
– Shaun
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
1
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.
– Shaun
1 hour ago
1
ok then i change the title....
– neelkanth
1 hour ago
|
show 1 more comment
1
The package did load. It returnedtrue.
– Shaun
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
1
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.
– Shaun
1 hour ago
1
ok then i change the title....
– neelkanth
1 hour ago
1
1
The package did load. It returned
true.– Shaun
1 hour ago
The package did load. It returned
true.– Shaun
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
1
1
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.
– Shaun
1 hour ago
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.
– Shaun
1 hour ago
1
1
ok then i change the title....
– neelkanth
1 hour ago
ok then i change the title....
– neelkanth
1 hour ago
|
show 1 more comment
1 Answer
1
active
oldest
votes
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 1 hour ago
ahulpke
7,007926
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
add a comment |
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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 1 hour ago
ahulpke
7,007926
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
add a comment |
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 1 hour ago
ahulpke
7,007926
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
add a comment |
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 1 hour ago
ahulpke
7,007926
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 1 hour ago
ahulpke
7,007926
answered 1 hour ago
ahulpke
7,007926
answered 1 hour ago
ahulpke
7,007926
answered 1 hour ago
ahulpke
7,007926
7,007926
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
add a comment |
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Ok thanks sir.... i will try this way and will tell you .....
– neelkanth
53 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
Yes Sir now it is working....thanks...
– neelkanth
49 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
But How i will know in future about The ATLAS name of any other group....
– neelkanth
48 mins ago
@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.
– ahulpke
14 mins ago
@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.
– ahulpke
14 mins ago
add a comment |
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1
The package did load. It returned
true.– Shaun
1 hour ago
@Shaun Thanks for edit...
– neelkanth
1 hour ago
@Shaun But not working to find Brauer Character...
– neelkanth
1 hour ago
1
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.
– Shaun
1 hour ago
1
ok then i change the title....
– neelkanth
1 hour ago