Bounding and unbounding higher extensions for SL2

We analyse the recursive formula found for various Ext groups for SL2(k)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)SL2(k) is at least exponential. In particular, View the MathML sourcemax{dimExtSL2(k)i(k,Δ(a))|a,i∈N} has (at least) exponential growth for all p . We also show that View the MathML sourcemax{dimExtSL2(k)i(k,Δ(a))|a∈N} for a fixed i is bounded.