Tautological bases of CoHA modules

2021/11/19 by Franzen, Hans, Sergey Mozgovoy, Mozgovoy, Sergey · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2111.10114

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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• Quiver moduli and quantum loop algebras

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