The degenerate affine walled Brauer algebra

Abstract

We define a degenerate affine version of the walled Brauer algebra, that has the same role plaid by the degenerate affine Hecke algebra for the symmetric group algebra. We use it to prove a higher level mixed Schur-Weyl duality for gl_N. We consider then families of cyclotomic quotients of level two which appear naturally in Lie theory and we prove that they inherit from there a natural grading and a graded cellular structure.