[GAP Forum] First cohomology question

Andrew Putman andyp at math.mit.edu
Thu Sep 18 05:54:17 BST 2008

Dear GAP Forum,

For some work I've been doing recently, I need to know the following.  

Let p be a prime and let g>1.  Denote by Sp(2g,Z/pZ) the symplectic group 
over Z/pZ and by V(2g,Z/pZ) the symplectic Lie algebra over Z/pZ with the 
adjoint action of Sp(2g,Z/pZ).  I need to calculate 
for some small p and g (it is known for large p and g).  

I am under the impression that GAP can do this, but I am having trouble 
figuring out how to do it.  I can figure it out for simpler 
representations of Sp(2g,Z/pZ), like the standard one on (Z/pZ)^{2g}, 
but I can't figure out how to get the adjoint representation.  Thank you 
very much for any help!


Andy Putman

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