arXiv subjects

Henry Scher

Publications and source records attributed to Henry Scher.

2 recordsLinked to original sources

arXiv2016

Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups

We calculate the rational cohomology of the commuting variety $X_{G, n}$ consisting of $n$-tuples of commuting elements of a compact reductive group $G$. This is done by studying a map from a related variety $Y_{G, n}$, 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.

math.RT↗

arXiv2015

The Bernstein-Sato b-function for the complement of the open $SL_n$-orbit on a triple flag variety

We calculate Bernstein-Sato b-functions for $f_{G^3}^λ$, a $SL_n$-invariant section of a line bundle on $SL_n/B \times SL_n/B \times \mathbb{P}^{n - 1}$ whose zero-set is the complement of the open $G$-diagonal orbit. The proof uses a similar calculation by Kashiwara of the b-function for $f^λ$, a $B^-$-semiinvariant section of a line bundle on $SL_n/B$ whose zero-set is the complement of the big Bruhat cell.

math.RT↗