1 results
Explicit calculations in an infinitesimal singular block of SLn
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 10 February 2022, pp. 19-52
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- Article
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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.
