The cocenter conjecture for the Gieseker variety and cyclotomic Hecke algebra

Let $\mathcal{L}(n,r)$ be the specified closed projective subvariety of the Gieseker space, let $K_{\mathcal{T}}(\mathcal{L}(n,r))$ denote its equivariant $K$-theory, and let the cocenter be the quotient of the cyclotomic Hecke algebra by its commutator subspace. Cocenter conjecture. There exists an isomorphism between the equivariant $K$-theory of $\mathcal{L}(n,r)$ and the cocenter of the cyclotomic Hecke algebra compatible with the natural pairings. This conjecture is presented as equivalent to the center conjecture, and no resolution is supplied here.