arXiv subjects

Maxim Kukol

Publications and source records attributed to Maxim Kukol.

2 recordsLinked to original sources

arXiv2026

Extended Future Tube Conjecture for Unipotent Subgroups

Let $\Omega$ be the Lorentz future cone in $\mathbb{R}^{d+1}$ with respect to the Lorentz product and let $T^M$ be the $M$-fold product of the future tube $T=\mathbb{R}^{d+1}+i\Omega$. The Lorentz group $\mathrm{SO}_0(1,d)$ acts diagonally on $T^M$, and its complexification $\mathrm{SO}(1,d)^\mathbb{C}$ acts on $\mathbb{C}^{(d+1)\times M}$. We prove that the domain $G^\mathbb{C}\cdot T^M$ is a Stein manifold for any connected unipotent subgroup $G$ of $\mathrm{SO}_0(1,d)$.

math.SG↗

arXiv2025

Hamiltonian Actions on Homogeneous Bounded Domains

We investigate Hamiltonian actions of non-compact Lie groups on a homogeneous bounded domain $X$. As a main result, we point out a Lie-theoretical condition for a closed Lie group $H$ of the automorphism group of $X$ which ensures that the symplectic reduction $\mu^{-1}(0)/H$ with respect to the momentum map $\mu$ at hand, is a Stein manifold. Moreover, for the class of connected subgroups of translations the quotient $(H^\mathbb{C}\cdot X)/H^\mathbb{C}$ is realized as a Siegel domain and we show that the symplectic reduction $\mu^{-1}(0)/H$ is biholomorphic to such a Stein quotient.

math.SG↗