To find Brauer Character for the special linear group SL(2,5) in GAP.












1














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.










share|cite|improve this question




















  • 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
















1














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.










share|cite|improve this question




















  • 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














1












1








1







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.










share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 1 hour ago

























asked 2 hours ago









neelkanth

2,0611927




2,0611927








  • 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














  • 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








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










1 Answer
1






active

oldest

votes


















2














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).






share|cite|improve this answer





















  • 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











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1 Answer
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1 Answer
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oldest

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active

oldest

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active

oldest

votes









2














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).






share|cite|improve this answer





















  • 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
















2














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).






share|cite|improve this answer





















  • 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














2












2








2






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).






share|cite|improve this answer












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).







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










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


















  • 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


















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