Explicit calculations in an infinitesimal singular block of SL n

Abstract Let $G= SL_{n+1}$ be defined over an algebraically closed field of characteristic $p > 2$ . For each $n \geq 1$ , there exists a singular block in the category $G_1$ -modules, which contains precisely $n+1$ irreducible modules. We are interested ‘lift’ this to $G_1T$ -modules. Imposing only mild assumptions on $p$ we will perform number calculations setting, including complete determination Loewy series for baby Verma modules and all possible extensions between In case where is extremely large, also explicitly compute indecomposable projective