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Algebraic construction of contragradient quasi-Verma modules in positive characteristic

Sergey Arkhipov
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Abstract

In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of the global Grothendieck-Cousin complex corresponding to the standard line bumdle ${\mathcal L}(λ)$ on the Flag variety of the algebraic group stratified by Schubert cells. We prove that the complex consists of direct sums of quasi-Verma modules for the highest weights of the form $w\cdotλ$ for various elements $w$ of the Weyl group.

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Sergey Arkhipov. 2001-05-05. Algebraic construction of contragradient quasi-Verma modules in positive characteristic. https://arxiv.org/abs/math/0105042

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