On a variety related to the commuting variety of a reductive Lie algebra.

Jean-Yves Charbonnel (1)

1 IMJ - Institut de Mathématiques de Jussieu

For a reductive Lie algbera over an algbraically closed field of charasteristic zero, we consider a borel subgroup $B$ of its adjoint group, a Cartan subalgebra contained in the Lie algebra of $B$ and the closure $X$ of its orbit under $B$ in the Grassmannian. The variety $X$ plays an important role in the study of the commuting variety. In this note, we prove that $X$ is Gorenstein with rational singularities.

Mots clés: polynomial algebra; complex; commuting variety; desingularization; Gorenstein; Cohen-Macaulay; rational singularities; cohomology

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

Jean-Yves Charbonnel. On a variety related to the commuting variety of a reductive Lie algebra.. 2016. ⟨hal-01178429v2⟩