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arXiv · 2111.10114

Tautological bases of CoHA modules

Hans Franzen·Sergey Mozgovoy
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Abstract

Given a quiver, we consider its cohomological Hall algebra (CoHA) as well as CoHA modules built of cohomology groups of non-commutative Hilbert schemes. We investigate cell decompositions of non-commutative Hilbert schemes and the corresponding (non-canonical) bases of CoHA modules. We construct canonical bases of CoHA modules, which consist of products of Chern classes of tautological vector bundles over non-commutative Hilbert schemes. This result generalizes classical results for Grassmannians and (partial) flag varieties.

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Hans Franzen, Sergey Mozgovoy. 2021-11-19. Tautological bases of CoHA modules. https://arxiv.org/abs/2111.10114

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