2020/06/23 by Charbonnel, Jean-Yves
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2006.12942
The commuting variety of a reductive Lie algebra \mathfrakg is the underlying variety of a well defined subscheme of \mathfrakg×\mathfrakg. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact.