Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
Ib´ anez N´ unez,Refined Harder-Narasimhan filtrations in moduli theory, arXiv:2311.18050, (2023)
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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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Hecke operators on symplectic surfaces and $\chi$-independence
Proves Toda's chi-independence conjecture and identifies BPS Lie algebra with tautological classes for one-dimensional Mukai vectors using Hecke operators and bialgebra structures.
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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.