Centralizers of nilpotent elements in basic classical Lie superalgebras in good characteristic

2022/10/24 by Leyu Han, Han, Leyu
Mathematics · #17B05 #17B20 #17B22 #17B25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2210.13155

openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrakg=\mathfrakg_0⊕\mathfrakg_1 be a basic classical Lie superalgebra over an algebraically closed field \mathbbK whose characteristic p>0 is a good prime for \mathfrakg. Let G_0 be the reductive algebraic group over \mathbbK such that Lie(G_0)=\mathfrakg_0. Suppose e∈\mathfrakg_0 is nilpotent. Write \mathfrakg^e for the centralizer of e in \mathfrakg and \mathfrakz(\mathfrakg^e) for the centre of \mathfrakg^e. We calculate a basis for \mathfrakg^e and \mathfrakz(\mathfrakg^e) by using associated cocharacters τ:\mathbbK^×→ G_0 of e. In addition, we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property for exceptional Lie superalgebras D(2,1;α), G(3) and F(4).

Related

• Reachable elements in basic classical Lie superalgebras
• The centralizer of a nilpotent section
• Centers of universal enveloping algebras of Lie superalgebras in prime characteristic
• The centralisers of nilpotent elements in classical Lie algebras
• Nilpotent centralizers and good filtrations