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Explicit calculations in an infinitesimal singular block of SLn
Published online by Cambridge University Press: 10 February 2022
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 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.
MSC classification
Primary:
20G05: Representation theory
Information
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 19 - 52
- Copyright
- Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
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