Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomological Hall algebras and perverse coherent sheaves on toric
  Calabi-Yau 3-folds   To a smooth local toric Calabi-Yau 3-fold $X$ we associate the Heisenberg
double of the (equivariant spherical) Cohomological Hall algebra in the sense
of Kontsevich and Soibelman. This Heisenberg double is a generalization of the
notion of the Cartan doubled Yangian defined earlier by Finkelberg and others.
We extend this "$3d$ Calabi-Yau perspective" on the Lie theory furthermore by
associating a root system to certain families of $X$.
  By general reasons, the COHA acts on the cohomology of the moduli spaces of
certain perverse coherent systems on $X$ via "raising operators". We conjecture
that the Heisenberg double acts on the same cohomology via not only by raising
operators but also by "lowering operators". We also conjecture that this action
factors through the shifted Yangian of the above-mentioned root system. We add
toric divisors to the story and explain the shifts in the shifted Yangian in
terms of the intersection numbers with the divisors. We check the conjectures
in several examples.

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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph