Lie Groups Seminar
A stratified smooth variety $M$ admits a Bruhat atlas (introduced by He,
Knutson and Lu) if it can be covered by open sets isomorphic to opposite
Bruhat cells in some Kac-Moody flag manifold via stratified isomorphisms.
Known examples include familiar stratified spaces such as the flag manifolds
$G/P$ and wonderful compactifications of groups. In this talk, I will show
that the wonderful compactification of the symmetric variety
$PSO(2n)/PSO(2n-1)$ admits a Bruhat atlas modelled by the Kac-Moody group
$SO(2n+2)$, using computations on a Bott-Samelson variety with wiring
diagrams as a combinatorial aid.