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 $\mathrm{\Lambda }$, one can associate a quiver Hecke algebras $R_{\beta }(K)$ and its cyclotomic quotient $R_{\beta }^{\mathrm{\Lambda }}(K)$ over $K$. It has been conjectured that the natural map from $R_{\beta }(K)$ to $R_{\beta }^{\mathrm{\Lambda }}(K)$ maps the center of $R_{\beta }(K)$ surjectively onto the center of $R_{\beta }^{\mathrm{\Lambda }}(K)$. 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.