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Loewy series of parabolically induced $G_1T$ -Verma modules

  • Abe Noriyuki (a1) and Kaneda Masaharu (a2)

Abstract

We show that the modules for the Frobenius kernel of a reductive algebraic group over an algebraically closed field of positive characteristic $p$ induced from the $p$ -regular blocks of its parabolic subgroups can be $\mathbb{Z}$ -graded. In particular, we obtain that the modules induced from the simple modules of $p$ -regular highest weights are rigid and determine their Loewy series, assuming the Lusztig conjecture on the irreducible characters for the reductive algebraic groups, which is now a theorem for large $p$ . We say that a module is rigid if and only if it admits a unique filtration of minimal length with each subquotient semisimple, in which case the filtration is called the Loewy series.

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