The equivariant K-theory of Gieseker varieties is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.
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The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.
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K-theory of Gieseker variety and type A cyclotomic Hecke algebra
The equivariant K-theory of Gieseker varieties is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra over the K-theory of a point.
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Additive categorification of the monoidal $\Lambda$-invariant
The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.