Algebraic construction of contragradient quasi-Verma modules in positive characteristic

By Sergey V. Arkhipov. 2001

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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 ${\mathcal L}(\lambda)$ 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 $w\cdot\lambda$ for various elements $w$ of the Weyl group.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cbda1584ecfe4eb06a19c7b5663027737f73fafe

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In Algebra and Number Theory

1. Volodymyr Mazorchuk
2. C. Stroppel
3. Jonathan Nilsson
4. Kaiming Zhao

In Geometry and Topology

1. Volodymyr Mazorchuk
2. C. Stroppel
3. Jonathan Nilsson
4. Vanessa Miemietz
5. Kaiming Zhao
6. Joshua Sussan
7. Ben Webster
8. Jonathan Brundan

In Mathematical Physics

1. Volodymyr Mazorchuk
2. C. Stroppel
3. Jonathan Nilsson
4. Vanessa Miemietz
5. Joshua Sussan

Citations in the corpus

• Some homological properties of the category O (2007, background): “For w ∈ W let Tw : O0 → O0 denote the corresponding Arkhipov’s twisting functor, see [Arkhipov 2004; Andersen and Stroppel 2003].”