I'm writing an algorithm in GAP to automate some easy calculations related to elements of prime order in groups that appear in the ATLAS. To automate the process, I need to access the character values for some irreducible complex representations of small degree so I can do some basic arithmetic on them.

Is there any way to access these without computing all of the irreducible characters using the function Irr(G)? Calling Irr(G) takes a very long time to run on my computer (on PSL(4,3), for example) and I really only need the two or three smallest irreducible representations.

Thanks in advance!


If the character table is in the ATLAS (or related) you can access it immediately by its name:


The long time you observe is presumably a call such as

gap> d:=CharacterTable(PSL(4,3));;
gap> Irr(d);

which stems from calculating the character table afresh from first principles. In this second case you might be able to start with some ad-hoc computations and hope that this gives certain low-degree characters, but there is no generic process that would get all low-degree characters quicker.

In short, unless you need the connection to the group, access the character tables by name, not from constructing a group first.


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