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arxiv: math/9805021 · v1 · submitted 1998-05-06 · 🧮 math.RT · math.AG

Equivariant D-modules

Ryoshi Hotta This is my paper
classification 🧮 math.RT math.AG
keywords groupmodulespartseveralsystemsactionalgebraicbasic
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The first part of these notes is devoted to an introduction to algebraic $D$-modules. Several basic notions are introduced. In the second part, $D$-modules with group action are treated. Several important examples in this situation are discussed in details. Particularly, the Harish-Chandra systems for group characters and the Gelfand generalized hypergeometric systems are our main topics.

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  1. Hypergeometric $\mathcal D$-modules and exponential sums for reductive groups

    math.AG 2024-11 unverdicted novelty 7.0

    Authors define hypergeometric exponential sums and sheaves for reductive groups, introduce hypergeometric D-modules, prove holonomicity and rank bounds, and use Fourier transforms to estimate the sums.