K-theory of Gieseker variety and type A cyclotomic Hecke algebra

We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys–Murphy center of the cyclotomic Hecke algebra, over the equivariant K-theory of a point. The construction is inspired by the proof of the Hikita–Nakajima conjecture for Gieseker spaces given by the first and third authors. We discuss consequences for the center of cyclotomic Hecke algebras and for specializations to q=1 and to roots of unity. In particular, we relate K-theory of affine type A quiver varieties with the centers of the corresponding blocks of specialized cyclotomic Hecke algebras. This last result strengthens the correspondences obtained by the second author in earlier work.