C\^ones nilpotents des super alg\`ebres de Lie orthosymplectiques

TL;DR

This paper explores the structure of odd nilpotent orbits in orthosymplectic Lie superalgebras, providing combinatorial insights, analyzing their closure relations, and presenting a desingularization of the nilpotent cone.

Contribution

It introduces a combinatorial interpretation of odd nilpotent orbits in osp(2n+1,2n), linking them to even orbits via the square map, and constructs a desingularization of the odd nilpotent cone.

Findings

Combinatorial interpretation of odd nilpotent orbits

Relationship between odd and even nilpotent orbits via the square map

A desingularization of the odd nilpotent cone

Abstract

We look at the odd nilpotent orbits of osp(2n+1,2n), giving a combinatorial interpretation which enables us, via the square map, to explain the link with even nilpotent orbits. We then study the closure ordering of the odd nilpotent orbits. Finally, we give a desingularization of the odd nilpotent cone.