Centers of centralizers of nilpotent elements in Lie superalgebras 𝔰𝔩(m|n) or 𝔬𝔰𝔭(m|2n)

Abstract

Let [Formula: see text] be the simple algebraic supergroup [Formula: see text] or [Formula: see text] over [Formula: see text]. Let [Formula: see text] and let [Formula: see text], where [Formula: see text] is considered as a superalgebra concentrated in even degree. Suppose [Formula: see text] is nilpotent. We describe the centralizer [Formula: see text] of [Formula: see text] in [Formula: see text] and its center [Formula: see text]. In particular, we give bases for [Formula: see text], [Formula: see text] and [Formula: see text]. We also determine the labeled Dynkin diagram [Formula: see text] with respect to [Formula: see text] and subsequently describe the relation between [Formula: see text] and [Formula: see text].