Algebra Seminar: Hu -- On the center of cyclotomic quiver Hecke algebras and cyclotomic Hecke algebras of type A

Jun Hu (Beijing Institute of Technology) 

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

Title: On the center of cyclotomic quiver Hecke algebras and cyclotomic Hecke algebras
of type A 

Abstract: Let n be a natural number 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 centre of R_beta(K) surjectively onto
the centre of R_beta^Lambda(K).  A similar conjecture claims that the centre of the
affine Hecke algebra of type A maps surjectively onto the center of its cyclotomic
quotient---the cyclotomic Hecke algebra of type G(l,1,n) over K.  In this talk I will
explain my proof of these two conjectures.