THE LOEWY STRUCTURE OF -VERMA MODULES OF SINGULAR HIGHEST WEIGHTS
2015 ◽
Vol 16
(4)
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pp. 887-898
Keyword(s):
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.
2014 ◽
Vol 14
(1)
◽
pp. 185-220
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2018 ◽
Vol 62
(2)
◽
pp. 559-594
2018 ◽
Vol 2019
(18)
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pp. 5811-5853
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2014 ◽
Vol 150
(12)
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pp. 2127-2142
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2014 ◽
Vol 58
(1)
◽
pp. 169-181
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2008 ◽
Vol 144
(4)
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pp. 849-866
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