Quiver Hecke algebras from Floer homology in Couloumb branches
Mina Aganagic, Ivan Danilenko, Yixuan Li, Vivek Shende, and Peng Zhou
TL;DR
This paper demonstrates that cylindrical KLRW algebras, which are important for cylindrical link homology theories, can be realized through Lagrangian Floer homology in Coulomb branches, confirming a homological mirror symmetry prediction.
Contribution
It establishes a novel connection between cylindrical KLRW algebras and Lagrangian Floer homology in Coulomb branches, confirming a homological mirror symmetry conjecture.
Findings
Cylindrical KLRW algebras are realizable via Floer homology.
Supports the homological mirror symmetry prediction.
Advances understanding of link homology theories.
Abstract
Homology theories categorifying quantum group link invariants are known to be governed by the representation theory of quiver Hecke algebras, also called KLRW algebras. Here we show that certain cylindrical KLRW algebras, relevant in particular for cylindrical generalizations of link homology theories, can be realized by Lagrangian Floer homology in multiplicative Coulomb branches. This confirms a homological mirror symmetry prediction of the first author.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology