To study the representation theory of a given algebra, one of the fundamental problems is to understand the center of the algebra. For semisimple Lie superalgebras (over complex numbers), one considers the center of the enveloping algebras. In this case, the center is described as certain invariant polynomials over the Cartan subalgebra through the Harish-Chandra homomorphism. Its analog for the affine Lie algebras was established by Feigin and Frenkel in the beginning of the 90s and plays a fundamental role in the geometric Langlands program. However, the generalization to the affine Lie superalgebras has been an open question since then. In this talk, I discuss our recent progress in describing the center based on the duality of the so-called W-superalgebras. The talk is based on a joint project with Drazen Adamovic.
