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THE LOEWY STRUCTURE OF
$G_{1}T$-VERMA MODULES OF SINGULAR HIGHEST WEIGHTS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 16 / Issue 4 / September 2017
- Published online by Cambridge University Press:
- 02 October 2015, pp. 887-898
- Print publication:
- September 2017
-
- Article
- Export citation
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Let
$G$ be a reductive algebraic group over an algebraically closed field of positive characteristic, 
$G_{1}$ the Frobenius kernel of 
$G$, and 
$T$ a maximal torus of 
$G$. We show that the parabolically induced 
$G_{1}T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan–Lusztig 
$P$- and 
$Q$-polynomials. We assume that the characteristic of the field is sufficiently large that, in particular, Lusztig’s conjecture for the irreducible 
$G_{1}T$-characters holds.
