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

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.

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, Dec 25 '18 at 08:45
m:=SL(2,5); creates a variable m which contains a group. "m" is a string which contains a character m. It has no connection to the variable m. Incidentally, "M" and "m" are both identifiers for the character table of the monster simple group, which then is retrieved from the library by CharacterTable("m"), but it has no known character table mod 2, so fail is returned. — Olexandr Konovalov, Dec 27 '18 at 09:46

score 3 · Accepted Answer · answered Dec 25 '18 at 09:06

3

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 09:06

ahulpke

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Ok thanks sir.... i will try this way and will tell you ..... – neelkanth Dec 25 '18 at 09:18
Yes Sir now it is working....thanks... – neelkanth Dec 25 '18 at 09:22
But How i will know in future about The ATLAS name of any other group.... – neelkanth Dec 25 '18 at 09:23
1

@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 Dec 25 '18 at 09:57
@ahulpkr thanks sir I will purchase this book ... – neelkanth Dec 25 '18 at 12:27
Sir I got a book with name “ Representation of groups ... a computational approach” ...is it the same book ??? – neelkanth Dec 25 '18 at 13:35
You can also take a look at the online version of the ATLAS here: http://brauer.maths.qmul.ac.uk/Atlas/v3/ – Bernhard Boehmler Jan 28 '19 at 11:25

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

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