TL;DR
This paper introduces algebraic D-modules, explores D-modules with group actions, and discusses key examples like Harish-Chandra systems and Gelfand hypergeometric systems, highlighting their structures and applications.
Contribution
It provides a comprehensive introduction to algebraic D-modules and detailed treatment of D-modules with group actions, including important examples and applications.
Findings
Detailed exposition of algebraic D-modules and their basic notions
Analysis of D-modules with group actions and their examples
Discussion of Harish-Chandra systems and Gelfand hypergeometric systems
Abstract
The first part of these notes is devoted to an introduction to algebraic -modules. Several basic notions are introduced. In the second part, -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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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory