Equivariant D-modules

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.

36 pages

Cited by in corpus (25)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• The rank of a hypergeometric system
• Algebraic aspects of hypergeometric differential equations
• Poisson traces, D-modules, and symplectic resolutions
• Euler and Laplace integral representations of GKZ hypergeometric functions
• Period Integrals and the Riemann-Hilbert Correspondence
• Period Integrals and Tautological Systems
• Confluent A-hypergeometric functions and rapid decay homology cycles
• Dualizing, projecting, and restricting GKZ systems
• Gevrey expansions of hypergeometric integrals I
• Slopes of a Hypergeometric System Associated to a Monomial Curve
• Laplace, Residue, and Euler integral representations of GKZ hypergeometric functions
• $\ell$-adic GKZ hypergeometric sheaf and exponential sums
• Irregular hypergeometric D-modules
• On the parametric behavior of A-hypergeometric series
• Logarithmic A-hypergeometric series
• $\ell$-adic Tautological Systems
• Gevrey and formal Nilsson solutions of $A$-hypergeometric systems
• Tautological systems and free divisors
• Bivariate hypergeometric D-modules
• Holonomic Systems for Period Mappings
• On the $b$-functions of hypergeometric systems
• Hypergeometric Functions for Projective Toric Curves
• Monodromies at infinity of confluent A-hypergeometric functions
• On Irregular Binomial $D$-modules