Explicit calculations in an infinitesimal singular block of SL_N

2018/05/11 by Hardesty, William
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.04614

Abstract

Let G= SL_n+1 be defined over an algebraically closed field of characteristic p > 2. For each n ≥ 1 there exists a singular block in the category of G₁-modules which contains precisely n+1 irreducible modules. We are interested in the lift of this block to the category of G₁T-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.

Related

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