2014/11/30 by Anne Moreau, Rupert W. T. Yu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Closure (psychology) #Jet (fluid) #Lie algebra #Mathematics #Mechanics #Nilpotent #Nilpotent group #Nilpotent matrix #Orbit (dynamics) #Physics #Political science #Pure mathematics #math.AG #math.RT
paper · pdf · doi:10.2140/pjm.2016.281.137
published as Pacific J. Math. 281 (2016) 137-183 · 39 pages in English. Final version, to appear in Pacific J. of Math
arxiv created 2015/09/01 · openalex publication_date 2016/02/09 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study in this paper the jet schemes of the closure of nilpotent orbits in a finite-dimensional complex reductive Lie algebra. For the nilpotent cone, which is the closure of the regular nilpotent orbit, all the jet schemes are irreducible. This was first observed by Eisenbud and Frenkel, and follows from a strong result of Musta\ut\ca (2001). Using induction and restriction of "little" nilpotent orbits in reductive Lie algebras, we show that for a large number of nilpotent orbits, the jet schemes of their closure are reducible. As a consequence, we obtain certain geometrical properties of these nilpotent orbit closures.