2012/10/09 by Karin Erdmann, Erdmann, Karin, Keith C. Hannabuss +3
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1210.2557
21 pages
arxiv created 2012/12/06 · arxiv updated 2012/12/07
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 \dim \Exti\SL2(k)(k, Δ(a))| a,i ∈ \N \ has (at least) exponential growth for all p. We also show that max \dim \Exti\SL2(k)(k, Δ(a))| a∈ \N \ for a fixed i is bounded.