12. MIKHAIL-V. IGNATYEV
Information acquired: 2025
MIKHAIL-V. IGNATYEV is an academic who published a paper in 2016 entitled Rea,, group orbits on flag ind-varieties of SL (âˆz, C). MIKHAIL-V. IGNATYEV published this work as part of a team: Ignatyev, Mikhail V.. Here is a description of this work: We consider the complex ind-group $G=SL ( infty, mathbb{C})$ and its real forms $G^0=SU( infty, infty)$, $SU(p, infty)$, $SL( infty, mathbb{R})$, $SL( infty, mathbb{H})$. Our main object of study are the $G^0$-orbits on an ind-variety $G/P$ for an arbitrary splitting parabolic ind-subgroup $P subset G$, under the assumption that the subgroups $G^0 subset G$ and $P subset G$ are aligned in a natural way. We prove that the intersection of any $G^0$-orbit on $G/P$ with a finite-dimensional flag variety $G_n/P_n$ from a given exhaustion of $G/P$ via $G_n/P_n$ for $n to infty$, is a single ($G^0 cap G_n$)-orbit. We also characterize all ind-varieties $G/P$ on which there are finitely many $G^0$-orbits, and provide criteria for the existence of open and close $G^0$-orbits on $G/P$ in the case of infinitely many $G^0$-orbits..