Quiver $\mathscr{D}$-modules and the Riemann-Hilbert correspondence

zbMATH Open1327.32019arXiv1505.05103MaRDI QIDQ2945870

Stephanie Zapf

Publication date: 15 September 2015

Abstract: In this paper, we show that every regular singular $mathscrD$-module in $mathbb{C}^n$ whose singular locus is a normal crossing is isomorphic to a quiver $mathscrD$-module - a $mathscrD$-module whose definition is based on certain representations of the hypercube quiver. To be more precise we give an equivalence of the respective categories. Our definition of quiver $mathscrD$-modules is based on the one of Khoroshkin and Varchenko. To prove the equivalence, we use an equivalence by Galligo, Granger and Maisonobe for regular singular $mathscrD$-modules whose singular locus is a normal crossing which involves the classical Riemann-Hilbert correspondence.

Full work available at URL: https://arxiv.org/abs/1505.05103

zbMATH Keywords

normal crossing singular locusquiver \(\mathcal D\)-moduleregular singular holomomic \(\mathcal D\)-module

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38)

Related Items (5)

DT-Invariants of Quivers and the Steinberg Character of GLn ⋮ Quantum Serre Theorem as a Duality Between QuantumD-Modules: Table 1. ⋮ On a class of holonomic \(\mathcal D\)-modules on \(M_n(\mathbb C)\) related to the action of \(\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n (\mathbb C)\) ⋮ Rigid modules and ICE-closed subcategories in quiver representations ⋮ D _n Dynkin quiver moduli spaces

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