The affine Hecke algebra has a remarkable commutative subalgebra corresponding to the coroot lattice in the affine Weyl group. Its nature is encoded in the Bernstein presentation and reveals important representation-theoretic properties of the algebra. If one considers categorifications of the Hecke algebra, for instance the diagrammatic category, the above subalgebra corresponds to a class of complexes in the homotopy category called Wakimoto sheaves, which can be seen as Rouquier complexes. In this talk I will introduce the affine Hecke algebra, the diagrammatic category and the objects mentioned above. Then I will describe some reduced representarives for Rouquier complexes and present some results about the extension groups between Wakimoto sheaves in affine type A1.
This video is part of the University of Georgia‘s Algebra seminar.
