Bounding and unbounding higher extensions for SL<inf>2</inf>

We analyse the recursive formula found for various Ext groups for SL2(k), k a field of characteristic p , and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of SL2(k) is at least exponential. In particular, max{dimExtSL2(k)i (k,Δ(a))|a,i∈N} has (at least) exponential growth for all p We also show that max{dimExtSL2(k)i(k,Δ(a))|a∈N} for a fixed i is bounded. © 2013 Elsevier Inc.