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.
Equivariant D-modules
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abstract
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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math.AG 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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Hypergeometric $\mathcal D$-modules and exponential sums for reductive groups
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.