## University of Sydney Algebra Seminar

# Jun Hu (Beijing Institute of Technology)

## Friday 11 August, 12-1pm, Place: Carslaw 375

## On the center of cyclotomic quiver Hecke algebras and cyclotomic Hecke algebras of type \(A\)

Let \(n\in\mathbb{N}\) and \(K\) be any field. For any symmetric generalized Cartan matrix \(A\), any \(\beta\) in the positive root lattice with height \(n\) and any integral dominant weight \(\Lambda\), one can associate a quiver Hecke algebras \(R_{\beta}(K)\) and its cyclotomic quotient \(R_{\beta}^{\Lambda}(K)\) over \(K\). It has been conjectured that the natural map from \(R_{\beta}(K)\) to \(R_{\beta}^{\Lambda}(K)\) maps the center of \(R_{\beta}(K)\) surjectively onto the center of \(R_{\beta}^{\Lambda}(K)\). A similar conjecture claims that the center of the affine Hecke algebra of type \(A\) maps surjectively onto the center of its cyclotomic quotient---the cyclotomic Hecke algebra of type \(G(\ell,1,n)\) over \(K\). In this talk I will explain my proof of these two conjectures.