Study of some orthosymplectic Springer fibers

Séverine Leidwanger (1) , Nicolas Perrin (1)

1 IMJ - Institut de Mathématiques de Jussieu

We decompose the fibers of the Springer resolution for the odd nilcone of the Lie superalgebra $\osp(2n+1,2n)$ into locally closed subsets. We use this decomposition to prove that almost all fibers are connected. However, in contrast with the classical Springer fibers, we prove that the fibers can be disconnected and non equidimensional.

Mots clés: Odd Nilpotent orbits; Springer fibers

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Séverine Leidwanger, Nicolas Perrin. Study of some orthosymplectic Springer fibers. 2010. ⟨hal-00459567⟩