Proposes and proves for 5D an expression for charge functions of odd-dimensional partitions whose poles mark addable and removable boxes.
Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
5 Pith papers cite this work, alongside 360 external citations. Polarity classification is still indexing.
5
Pith papers citing it
360
external citations · Pith
abstract
We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves or functions. In order to take into account the potential we introduce a generalization of theory of mixed Hodge structures, related to exponential integrals. Generating series of our Cohomological Hall algebra is a generalization of the motivic Donaldson-Thomas invariants introduced in arXiv:0811.2435. Also we prove a new integrality property of motivic Donaldson-Thomas invariants.
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UNVERDICTED 5representative citing papers
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
Constructs t-exact faithful realization functors from exponential sheaves to D-modules and a universal Fourier transform that commutes with classical FTs and preserves purity.
Motivic Hall algebra geometry and moduli stack correspondences recover Auslander-Reiten sequences and the Auslander-Reiten quiver.
citing papers explorer
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Charge functions for odd dimensional partitions
Proposes and proves for 5D an expression for charge functions of odd-dimensional partitions whose poles mark addable and removable boxes.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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Realizations of exponential sheaves and Fourier transform
Constructs t-exact faithful realization functors from exponential sheaves to D-modules and a universal Fourier transform that commutes with classical FTs and preserves purity.
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Hall Geometry and Auslander-Reiten Quiver
Motivic Hall algebra geometry and moduli stack correspondences recover Auslander-Reiten sequences and the Auslander-Reiten quiver.