The Harish-Chandra isomorphism for reductive symmetric superpairs

We consider symmetric pairs of Lie superalgebras and introduce a graded Harish-Chandra homomorphism. Generalising results of Harish-Chandra and V. Kac, M. Gorelik, we prove that, assuming reductivity, its image is a certain explicit filtered subalgebra J( $ \mathfrak{a} $ ) of the Weyl invariants on a Cartan subspace whose associated graded gr J( $ \mathfrak{a} $ ) is the image of Chevalley’s restriction map on symmetric invariants. In contrast to the known cases, J( $ \mathfrak{a} $ ) is in general not isomorphic to gr J( $ \mathfrak{a} $ ).