English

Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups

Representation Theory 2016-08-08 v1

Abstract

We calculate the rational cohomology of the commuting variety XG,nX_{G, n} consisting of nn-tuples of commuting elements of a compact reductive group GG. This is done by studying a map from a related variety YG,nY_{G, n}, which has easily calculated cohomology. The proof studies the fibers of the map and uses the Vietoris-Begle theorem to prove that the induced map on rational cohomology is an isomorphism.

Keywords

Cite

@article{arxiv.1608.01743,
  title  = {Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups},
  author = {Henry Scher},
  journal= {arXiv preprint arXiv:1608.01743},
  year   = {2016}
}