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

Explicit calculations in an infinitesimal singular block of SLn

Explicit calculations in an infinitesimal singular block of SL_n